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Why the Buddha abandoned asceticism
It is commonly known that the Buddha decided that asceticism does not lead to enlightenment, but less common is the reason why given. From Ajahn Brahm's book Mindfulness, Bliss, and Beyond, it appears as though the Buddha abandoned asceticism because eating well was necessary to pursue the jhānas and the Middle Way:

once the Bodhisatta realized that jhāna was the way to enlightenment
  (MN 36,31), he immediately recognized that it was impractical to
  attain jhāna with an emaciated body so began eating well.

Where in MN 36 do we find this reasoning? Is there general agreement in Buddhism that this is indeed why the Buddha decided to give up asceticism?

That's interesting because didn't he already master the jhanas?

@Uilium the Buddha may have studied something close to jhana (MN 26,16; MN 36,31; 52,4-7, 64,9-12 with teachers but these didn't lead to his awakening. It was his memory of jhana as a child under the rose-apple tree MN 36 which preceded his entry into jhanas 1-4 and his awakening

When did he find out about the 3 characteristics?

The following findings most directy answer my original question.
An explanation of why the Buddha abandoned asceticism in favor of the Middle Way is given by Bhikku Bodhi in The Noble Eightfold Path -

The other extreme is the practice of self-mortification, the attempt to gain liberation by afflicting the body. This approach may stem from a genuine aspiration for deliverance, but it works within the compass of a wrong assumption that renders the energy expended barren of results. The error is taking the body to be the cause of bondage, when the real source of trouble lies in the mind—the mind obsessed by greed, aversion, and delusion. To rid the mind of these defilements the affliction of the body is not only useless but self-defeating, for it is the impairment of a necessary instrument.
...
Aloof from these two extreme approaches is the Noble Eightfold Path, called the middle way, not in the sense that it effects a compromise between the extremes, but in the sense that it transcends them both by avoiding the errors that each involves. The path avoids the extreme of sense indulgence by its recognition of the futility of desire and its stress on renunciation.
...
But the practice of renunciation does not entail the tormenting of the body. It consists in mental training, and for this the body must be fit, a sturdy support for the inward work. Thus the body is to be looked after well, kept in good health, while the mental faculties are trained to generate the liberating wisdom. That is the middle way, the Noble Eightfold Path, which “gives rise to vision, gives rise to knowledge, and leads to peace, to direct knowledge, to enlightenment, to Nibbāna.”

In MN 53 Sekha Sutta The Disciple in Higher Training, the Buddha emphasizes moderation in eating, and there are at least several other suttas in MN where the Buddha repeats the same.

“And how is a noble disciple moderate in eating? Here, reflecting wisely, a noble disciple takes food...only for the endurance and continuance of this body, for ending discomfort, and for assisting the holy life, considering: ‘Thus I shall terminate old feelings without arousing new feelings and I shall be healthy and blameless and shall live in comfort.’ That is how a noble disciple is moderate in eating.
MN 53 Sekha Sutta The Disciple in Higher Training

Ven. Ayya Khema has repeated this last quote in several of her dhamma talks (for example).
Also thanks to ChrisW for his answer.

one might consider asceticism a form of seeking. whereas the Buddha taught surrender to what is.

Maybe MN 26 is more relevant: towards the end of it, the Five ask questions like,

When this was said, the group of five monks replied to me, 'By that practice, that conduct, that performance of austerities you did not attain any superior human states, any distinction in knowledge & vision worthy of a noble one. So how can you now — living luxuriously, straying from your exertion, backsliding into abundance — have attained any superior human states, any distinction in knowledge & vision worthy of a noble one?'

... and afterwards, the end of the sutta is of their being taught the various jhanas.

There may be somewhere where it's stated as a positive, i.e. "eating well was necessary to pursue the jhānas and the Middle Way" -- I think I've read something like that, but I don't remember whether that's a direct quote or an indirect paraphrase.
The only versions I've found at the moment are expressed as a double-negative, not as a positive, i.e. that "utmost austerity is not the way"; for example from this translation of the (non-canonical) Introduction to the Jâtaka,

And the Future Buddha, thinking, "I will carry austerity to the uttermost," tried various plans, such as living on one sesamum seed or on one grain of rice a day, and even ceased taking nourishment altogether, and moreover rebuffed the gods when they came and attempted to infuse nourishment through the pores of his skin. By this lack of nourishment. his body became emaciated to the last degree, and lost its golden color, and became black, and his thirty-two physical characteristics as a great being became obscured. Now, one day, as he was deep in a trance of suppressed breathing, he was attacked by violent pains, and fell senseless to the ground, at one end of his walking-place.
...
Now the six years which the Great Being thus spent in austerities were like time spent in endeavoring to tie the air
  into knots. And coming to the decision, "These austerities are not the way to enlightenment," he went begging through villages and market-towns for ordinary material food, and lived upon it. And his thirty-two physical characteristics as a great being again appeared, and the color of his body became like unto gold.
Then the band of five priests thought, "It is now six years that this man has been performing austerities without being able to attain to omniscience. And how much less can he be expected to do so in future, now that he has again taken to ordinary material food begged from town to town! He has become luxurious, and given up the Struggle. For us to look for any benefit to come from that quarter would be as reasonable as if a man were to imagine he could bathe his head in a dew-drop. We will have nothing more to do with him." With that they took their bowls and robes, and left the Great Being, and going eighteen leagues off, entered Isipatana.

There are suttas which describe or recommend an attitude towards food (I expect there are in the vinaya too), for example from the Bhikkhuni Sutta,

'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said. And in reference to what was it said? There is the case, sister, where a monk, considering it thoughtfully, takes food — not playfully, nor for intoxication, nor for putting on bulk, nor for beautification — but simply for the survival & continuance of this body, for ending its afflictions, for the support of the holy life, [thinking,] 'Thus will I destroy old feelings [of hunger] and not create new feelings [from overeating]. I will maintain myself, be blameless, & live in comfort.' Then he eventually abandons food, having relied on food. 'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said, and in reference to this was it said.

@avatarKorra I think it's typical to not teach doctrine that isn't conducive to enlightenment (e.g. Simsapa Sutta etc.).

Your last quote on attitude towards food continues to be one of the most helpful I've read. It would be nice to find more like it.

@avatarKorra I think the Brahmana Sutta is a bit like it, not specifically about food but about desire (chanda).

Also I think that (people say that) the focus or subject (the object) of meditation (recommended by the Buddha) is "letting go". Food is a bit exceptional/unusual, in that (like clothing, at least minimal clothing), it's considered a necessity ... that can make it difficult (as an object of greed) because (unlike other objects of greed which may be abandoned) you have to live with it.

Though it may not be obvious, my motivation for the OP had to do with abandoning food as a form of craving. Which is why I found the above quote so helpful. It seems certain afflictions related to overconsumption of food could be prevented if more people approached food this way.

And it seems to me that the reason the object of meditation is  'letting go', is because it's understood to be the most succinct instruction for abandoning craving - i.e. the cessation of dukkha,  the Third Noble Truth.

And I'd think it's possible that food can be taken in a way without craving, just as air is taken to breathe. Although the Buddha still had to sleep, rise, and get food, these were probably handled as just a response to the process of being alive, without any concepts of craving. just like breathing.

I don't think it was just like breathing, food has taste and one still has preference over one type of food due to body response, bud response et cetera. With abandoning the body responses as in asceticism one cannot abandon the taste and body's reaction to food. In my opinion such abandonment is unwise. There still has to be mindful consumption with focus on taste, without suppressing it, otherwise it's just unnecessary torturing yourself again. We don't have to go back to square one.

We are, in the end, talking tanha here that is root of unwholesomeness and the cause of dukkha. It is enough what the passage says - severe under eating causes suffering and body agony, while overeating by habits of mindless self indulgence and addiction, other than dissatisfaction - causes suffering and body agony.

here's a precise link to relevant portion of the MN 36
https://suttacentral.net/en/mn36/36-42
the discovery of the middle way is not only manifested in the decision to resume eating and stop tormenting the body because austerities impede entering the jhana, but primarily in my opinion in the actual realization that the pleasure of jhanas is permissible and desirable because it's not sensual, only then came the understanding of incompatibility of severe asceticism with jhanas
this positions the Dhamma halfway between the practices of ascetics who avoided any kind of pleasure, being of the opinion that pleasure in future lives, or even liberation, is secured with suffering in this life (like the jains), and indulgence in low carnal sensuality

Didn't the Bodhisattva master the Jhanas with teachers before his remembering about Jhana states as a child while practicing extreme asceticism? What am I missing here?
The Middle Way is not eating extremely well and it is not eating extremely little. The middle way is in the middle of those two extremes so the Buddha was a mild ascetic or middle way ascetic.

In MN 36:33 (i 247) the Buddha says: "I considered, 'It is not easy to attain that pleasure with a body so excessively emaciated. Suppose I ate some solid food - some boiled rice and porridge.'" (Nanamoli and Bodhi, Middle Length Discourses of the Buddha, p. 340). What is especially interesting here is that the Buddha explicitly identifies the practice of the path with the experience of wholesome pleasure, as against the pain of his previous asceticism.


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The mind during Shikantaza
In Soto-Zen Buddhism there is a sitting meditation known as Shikantaza which is the art of just-sitting. My question, what techniques are given to Soto-Zen practitioners to prevent the mind from being "sticky" or "stuck" during Shikantaza. For example,

I have been told by some practitioners that they would call sight, sound, taste, touch, smell and mind as objects. By referring to the six sense organs as objects they disconnect themselves from the object to prevent the formation of subject. Although it sounds interesting that doesn't sound like, at least by what I've read, as Shikantaza.
Another practitioner told me they simply listened to silence or emptiness. This reminded me of Eckhart Tolle's meditation instructions especially given in his book "Stillness Speaks". The problem I find through this method is the practitioner is focusing on an object, as Lao tzu mentioned in his book the "Tao Te Ching"; the form which is formless. Also, Dogen encouraged the sitter to just sit with no attention to a single object. Concentration on emptiness is neglecting sitting and the original face.
Finally, another practitioner explained he would simply try to keep his attention centered as if he were sitting inside of a dome. That is, trying to be aware of the world and his thoughts while building a kind of cushion between himself and object. Almost but not exactly a combination of the first two.

Therefore, what are the steps Soto-Zen practitioners are encouraged to take in order to practice Shikantaza. To clarify, I'm not interested in physical postures such as sitting, hand positions, the position of the tongue, etc... but rather, what is the sitter doing with his/her mind and the steps they are taking to separate subject from object.

Treeleaf Soto-Zen center online has a systematic breakdown for doing Shikantaza meditation. If anyone is interested in listening to their videos to summarize their data here is a link: http://www.treeleaf.org/for-new-comers-and-about-treeleaf/

Look, there is nothing special about Shikantaza or any other type of meditation. If you ask me honestly, I say that meditation is for fun really. You don't do it to achieve anything. In fact the idea is to let everything be. And NOT achieve anything. No "Nirvana", No "Moksha", No "separation", No "clinging" or whatever labels we like to create.
There is really no answer to this question apart from experience. You just sit and go on with whatever happens, your physical and mental sensations. Until they cease (or not). The moment you start thinking anything about it or whatever to do about it, the point is lost.
What I mean is whatever you are thinking right now about the way to do it, or "am I doing it right?" or "what should I focus on?" or such like questions are mere thoughts and are invalid.

The nature of consciousness is it always has an 'object'. This is similar to if a very loud noise occurs; hearing the loud noise cannot be avoided. Consciousness of the loud noise happens automatically.
If a practitioner 'just sits', i.e., does not think or does not exercise intention/volition apart from 'just sitting', then the mind will automatically (primarily) be aware of the silence. Then objects, such as sounds may enter consciousness. Or, more predominantly, objects such as the in & out breathing may become the dominant sense object of consciousness. Similar to a loud noise, consciousness cannot avoid continuously experiencing the in & out breathing, jhana, etc. It will be automatic.
If the mind is allowed to wander in thoughts, certainly this cannot be 'just sitting' since it would be 'sitting & thinking' rather than 'just sitting'. Allowing the mind to wander in thought is different to continuously experiencing in & out breathing since the mind can control/stop thoughts but cannot control/stop breathing.
'Just sitting', I imagine, is just sitting. Thus, intention operates for the sole purpose of just sitting. Since thinking is not 'just sitting', the mind must act to maintain a state of just sitting.
'Thinking' is not 'just sitting'. Acting to stop thinking is also not 'just sitting'. But once both thinking & acting to stop thinking stop, there will be only the state of 'just sitting'.
Therefore, there is say 'the path' to achieve 'just sitting' and the actual achievement of 'just sitting', which are two different things.
Once 'just sitting' is achieved, the mind will automatically be enlightened by the 10,000 things.

I appreciate the answer you gave but I'm afraid it doesn't really answer my question. The answer you gave for object is true for formations (such as the world we see), but it's not what is meant in Soto-zen.  The only real shikantaza statement i can really find is, "But once both thinking & acting to stop thinking stop, there will be only the state of 'just sitting'."

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Are philosophers today misunderstanding 'emptiness' because of a new metaphysics?
From an article about Heidegger,

The beginning of this story, as told by Heidegger especially in the Nietzsche lectures, is the end, the completion of philosophy by its dissolution into particular sciences and nihilism—questionlessness of being, a dead end into which the West has run. Heidegger argues that the question of being would still provide a stimulus to the research of Plato and Aristotle, but it was precisely with them that the original experience of being of the early Greeks was covered over... For the later Heidegger, “western philosophy,” in which there occurs forgetfulness of being, is synonymous with “the tradition of metaphysics.” Metaphysics inquires about the being of beings, but in such a way that the question of being as such is disregarded, and being itself is obliterated. The Heideggerian “history of being” can thus be seen as the history of metaphysics, which is the history of being’s oblivion.

Is this itself reason to suspect that philosophers like Plato, by which I mean contemporary thinkers who are paid to publish philosophy (including I suppose self help authors and some aspects of psychology) are bound to misunderstand the concept of emptiness? When the Buddha taught, the history of Being, metaphysics, had not yet, it seems, begun.
Are philosophers and people in general misunderstanding the terminology the Buddha used, perhaps because he lived at a time before 'Being' when there was only 'world' -- etc..

Many people in general misunderstand the terminology the Buddha used, including Buddhists & even translators. If these people misunderstand the terminology then what is to be expected of Western philosophers?
About 'being', the Pali scriptures report the Buddha discussed this word at length. For example, in the core doctrine of Dependent Origination, the notion of 'beings' is central to the meaning of the word 'birth' ('jati').

And what is birth? Whatever birth, taking birth, entering, coming-to-be, coming-forth of the various beings in this or that group of beings based on the appearance ('look'; 'features') of aggregates & appropriation of the sense spheres, that is called birth.

The word 'being' ('satta') refers to an internally generated 'view' of 'self' or 'persons' (see Satta Sutta & Vajira Sutta below).
Although 'beings' in these suttas is described as a mental state or mental view, most Buddhists & people regard 'beings' meta-physically, i.e., as an organism.
Similarly, most people & Buddhists regard the word 'birth' ('jati') meta-physically, rather than the meaning in the Indian languages of 'social & self identity' (see Wiki).
As for 'emptiness' ('sunnata'), it is defined as the absence of "self".
In Pali Buddhism, 'being' & 'emptiness' are opposite things however both can exist in the human experience; 'being' arising from ignorance & emptiness discerned by enlightened clear seeing.
Most crucially, the Buddha was not a philosopher but, instead, a 'Spiritual Doctor'. The Buddha had only one sole concern, namely, the ending or curing of suffering.
For the Buddha, the arising of 'being', i.e., the arising of 'ego' or 'self', is the arising of suffering. For example, a new born child has no idea of 'self' but later develops ideas of 'myself' based on cravings for things (such as food, comfort, love, pleasures, etc). These cravings are sufferings thus the manifestation of 'being' is always from the manifestation of suffering (refer to Vajira Sutta below).

'A being,' lord. 'A being,' it's said. To what extent is one said to be 'a being'?"
Any desire, passion, delight, or craving for form, feeling, perceptions, mental fabrications &/or consciousness, Radha: when one
  is caught up there, tied up there, one is said to be 'a being.'
Satta Sutta

~~~

Why now do you assume 'a being'? Mara, have you grasped a view? This is a heap of sheer constructions: Here no being is found.
Just as, with an assemblage of parts, The word 'chariot' is used, So, when the aggregates are present, There's the convention 'a being.'
It's only suffering that comes to be, Suffering that stands and falls away. Nothing but suffering comes to be [when 'being' comes to be],
  Nothing but suffering ceases [when 'being' ceases].
Vajira Sutta

~~~

And what is the emptiness mind-release? There is the case where a monk, having gone into the wilderness, to the root of a tree, or into
  an empty dwelling, considers this: 'This is empty of self or of
  anything pertaining to self.' This is called the emptiness
  mind-release.
Mahavedalla Sutta

~~~

Insofar as it is empty of a self or of anything pertaining to a self: Thus it is said, Ananda, that the world is empty.
And what is empty of
  a self or of anything pertaining to a self? The eye is empty of a self
  or of anything pertaining to a self. Forms... Eye-consciousness...
  Eye-contact is empty of a self or of anything pertaining to a self.
The ear is empty...
The nose is empty...
The tongue is empty...
The body is empty...
The intellect is empty of a self or of anything pertaining to a self. Ideas... Intellect-consciousness... Intellect-contact is empty
  of a self or of anything pertaining to a self. Thus it is said that
  the world is empty."
Suñña Sutta

didn't really answer my question very directly, just seems to repeat a well known fact, that there is an emptiness of self. EDIT may help me think tho, cheers :)

thanks. this is a Buddhist forum therefore some contributors, such as myself, may know very little, possibly nothing, about Western philosophy. In summary, the Buddha taught the arising of 'being', i.e., the arising of 'ego' or 'self', is the arising of suffering. For example, a new born child has no idea of 'self' but later develops ideas of 'myself' based on cravings for things (such as food, comfort, love, pleasures, etc). These cravings are sufferings thus the manifestation of 'being' is always from the manifestation of suffering. Did Heidegger discuss the 'suffering of being'?

there's works contrasting heidegger and buddhism, but mahayana. not being able to read sanskrit, or really begin a sustained practice, i've read  a fair amount of philosophical scholarship on buddhism. also, i studied philosophy at uni. think that these overlaps just confused me...

I did my best to fix my answer for you.

I fixed it more.

good answer, tho it's a shame you aren't familiar with the academic tradition i mention. it's been a while since i read these, but i felt there was a lacuna there, and not merely because their practice was off!

The term 'misunderstanding' does not has the same meaning for a philosopher and a Buddhist. From the Buddhist perspective misunderstanding something means not seeing with one's own mind, not being able to see empirically. As for most philosophers, understanding only requires the ability to understand language and being able of logical analysis. Metaphysics is mostly subject to speculations about what is 'meta' (after, behind) 'physics' (empirically perceivable nature). I'm sure there are exceptions, i.e. Aristotle is said to be a big empiricist, but in Buddhism there's the big difference that words and terminology are useless.
As for misunderstanding the concept of emptiness, in Buddhism concepts don't really exist because you can't experience them (you can only experience thinking itself, you can't experience 1 + 1 = 2 for example), but emptiness is claimed to be a real experience. That being said, Buddhists would rather speak about the emptiness of concepts, claiming that theoretical knowledge won't bring you any insight. This is probably not a satisfying answer for you particular question, but since this is the Buddhist SE I hope it's good enough...
A suitable quote from Ajahn Chah:

If you don’t practice you won’t know. Frankly speaking, you
  won’t know the Dhamma by just reading it or studying it. Or
  if you do know it your knowledge is still defective. For example, this spittoon here. Everybody knows it’s a spittoon but they
  don’t fully know the spittoon. Why don’t they fully know it? If
  I called this spittoon a saucepan, what would you say? Suppose
  that every time I asked for it I said, “Please bring that saucepan
  over here,” that would confuse you. Why so? Because you don’t
  fully know the spittoon. If you did there would be no problem.
  You would simply pick up that object and hand it to me, because
  actually there isn’t any spittoon. Do you understand? It’s a spit-
  toon due to convention. This convention is accepted all over the
  country, so it’s spittoon. But there isn’t any real “spittoon.” If
  somebody wants to call it a saucepan it can be a saucepan. It
  can be whatever you call it. This is called “concept.” If we fully
  know the spittoon, even if somebody calls it a saucepan there’s
  no problem. Whatever others may call it we are unperturbed because we are not blind to its true nature. This is one who knows
  Dhamma

not a bad reply, thanks. a bit too anti conceptual to really accept tho :) actually, i agree with one of the answers which claims that Heidegger is completely off here. to say that the buddha came before X, so wasn't properly thinking like Xs, is fundamentally a misunderstanding

One can hardly say "philosophers today", as philosophy itself is a wide field of activities; it can mean academic philosophy (which is publish-or-perish style of life, plus perhaps thinking "I am special because I do something which is profound and special" -- but that's the same for physicists or biologists) or conceptual reflection of experience. But it matters what experience is reflected, at what level, and what is the reflection supposed to bring.
So I will discuss philosophy as something extra-theoretical.
I happen to disagree with Heidegger in his accusations of metaphysics. Metaphysics (reflection) and being (contemplation) are orthogonal, but it is important that metaphysical reflection is based on contemplation (rather than delusion). There are contemplative geniuses, who are also masters of conceptualization of that experience (think of Nagarjuna, Dogen or Aquinas) all while knowing that it does not replace the experience itself (or being; ironically, it was Aquinas who re-introduced the concept of being (esse) into the western tradition). There are also great contemplatives who don't do conceptualization (for whatever reason) -- think of masters like Joshu, or John of the Cross if you wish, or a big amount of monks who never wrote anything.
There are also people who have little access to being (no contemplation), yet write papers/books about it -- unaware of their own ignorance. And there are people who are out of touch with being, and don't conceptualize.
The concept of emptiness (just like the concept of being) is pointing at something more than the concept itself, and its understanding comes through contemplative practice (which is called vipassana in buddhism). What I can suggest is that you do a vipassana retreat (I mean, 2 weeks or more), it is really worth it for many reasons, and then you will be able to see better if what they write about Wittgenstein & Nagarjuna and so on makes sense. A good question is what is the use of reading those papers anyway :)
(PS: I am a philosophy major and have later experience with vipassana.)

it's not a pun, it's what the term means https://en.wiktionary.org/wiki/metaphysics

one can say "philosophy today" very easily, same as 'physics today' 'psychology today', etc.. the 'today' qualification may seem blurred, but "philosophy" has a history, so i don't see why not. it's you that is punning, i think. i get what you mean, but i did say 'like Plato' so am not sure why

I changed the word to "accusation", hope that is clearer; Heidegger had a problem with it which he formulated repeatedly in the course of his life, and I think that it (validly) targets only a specific flavor of metaphysics. As for philosophy today, yes, you can say that, but as soon as you want to talk about something specific, you have to start making distinctions. Can you say that 'psychology today' does (not) understand mindfulness?

doubt i'll get a better answer tho, so i accept what i understand of your claim, that there are obvious overlaps between buddhist philosophy and everyday experience etc..

yeah i think you can say that. i didn't mean to make a universal claim about the literature, even, let alone every philosopher, etc. obviously i was being a little too clever in the question, but it seemed so neat

I don't claim there are necessarily overlaps of buddhist/western philosophy; the basis of contemplation is reality when observed very carefully (I would not say "everyday" experience; vipassana means "seeing clearly/distinctly/truth" or things as they are.). Whether it leads to conceptual similarities is an open question which hardly has a theoretical answer.

whether or not buddhists are observing anything special, i think you need to change your answer if you are not claiming that your term "contemplation" has its analogue in philosophy. i have unaccepted your question as it is not clear enough. i don't want to discuss semantics, i just want a well reasoned or informative reply. i think you are deliberately misunderstanding me if you say you didn't know what i meant by 'philosophy today'. alternatively, if it's unclear, leave a comment

as to the pun thing... he's using the term correctly (no?) and any mixing up of senses is just not doing the work. i've seen people claim that heidegger's philosophy is based on a pun, but not on 'metaphysics' and i'm fairly unsure that this joke about 'nothing' is even meant seriously by his critics. if he's not mixed up, then any punning has absolutely nothing to do with the matter at hand. good luck in your philosophy degree, tho. i too majored in philosophy. what's important is that you keep studying it :)

Oh, sorry about "pun", forget about it, that was my poor command of English. I don't remember ever seeing something humorous in his texts. Late Hggr was appreciative of eastern traditions, so actually the best way to study Hggr is to do vipassana :) Good luck and don't forget the practice :)

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Did I describe the following concept correctly?
In a discussion, my meditation leader was talking about people who cannot control their cravings and wants, who are easily subjected to actions based on their whims and wants of their anger. He associated these people with having akusala thoughts. He could not find the English word to describe the person, and so I gave him the word impulsive as a way to describe these people.
Was this the right word to use, and is there a better word that I could have used?

You're asking for an English translation, a word equivalent to akusala (and asking whether "impulsive" is a good translation/description).

@ChrisW more asking if it's a good translation for akusala, yes.

A related question: Does 'kusala' (skillful) also mean 'wholesome' and 'morally good'?

Also, just as an FYI, he is not talking about the kinds of people but the kinds of thoughts which is an important distinction, as all beings are worthy of love and certainly worthy of compassion.

@sova I am sure he was looking to describe those people themselves.

@tuskiomi well that would be strange because those qualities are not inherent within us, but rather fleeting and unfavorable circumstances that can be swept away through dharma practice.

@sova interesting

There's a definition of kusala here:

kusala: characterizes all which has pleasant and happy results: advantageous, meritorious, skilful, virtuous, morally good, good, right, prosperous, salutary, skilful. Especially used in its moral sense.
The Commentary defines the term as having three meanings:

(psychologically, spiritually) healthy
blameless
productive of pleasant and favourable results.

Kusala can also be defined as what arises on the basis of the three kusala·mūlas. In terms of action, ten main kusala actions are listed and called together kusala·kamma·pathas.

I think 'impulsive' isn't exactly the same as akusala.
Let's look at an antonym of 'impulsive', for example "cautious". Or @slova's answer suggests "slow" and "prudent". I imagine that someone who is not impulsive might think twice before speaking, look both ways before crossing the street, save their money instead of spending it ... but that (e.g. hoarding their money) is not necessarily kusala.
Or let's consider for example Siddhārtha Gautama's deciding to leave home: that story might (or might not) seem a bit "impulsive", but we shouldn't call it akusala.
Being impulsive might be one example of akusala (e.g. losing your temper and suddenly killing someone in anger), but there are other forms of akusala which are not impulsive (e.g. carefully planning a crime for a long time before doing it).
Also I hope that there are some forms of being impulsive that are not very akusala (for example impulsively deciding to try to help someone else, being impulsively kind).

You said that your "leader was talking about people who cannot control their cravings and wants, who are easily subjected to actions based on their whims and wants of their anger".
Things like cravings and anger (and ignorance) are known akusala-mūla which are translated/called/known in English the "three poisons" or "three unwholesome roots", also "three roots of evil" and "the three unwholesome mental states". In that phrase, akusala is translated as "unwholesome" or even evil.
As @sova mentioned in a comment it's the mental state (e.g. of anger) that's unwholesome, or the result (like the tree which grows from the "root") that's unwholesome.

That's a great translation.  Other words that may fit like impulsive

hasty
imprudent

@ChrisW mentions in a comment that kusala means skillful, so a +kusala would mean the negation of kusala (if you look at how sanskrit works), thus another word may be unskillful  and it sounds like your meditation friend was trying to expound on what that term actually means.
Many words have nuances that can become lost in translation, so sometimes it is good to leave words untranslated, or look at how they were constructed.  For example: we could not say "pulsive" as the negation of "impulsive" even though "possible" and "impossible" have the same relationship as "kusala" and "akusala" -- it just depends.  Again, good translation, but be open to the idea that not everything need be translated (and thus nuance can be ushered into a new language body and preserved)

in my opinion it's a poor translation because it doesn't account for the ethical significance of consequences this type of action brings about and which is actually envisaged in the meaning of the words kusala/akusala, there's no contradiction between impulsiveness of action and its being kusala

@БаянКупи-ка well, provide an alternative then! =)

i believe extant English sutta translations provide good enough alternatives, in fact it's the rendering impulsive which is alternative in my opinion

@БаянКупи-ка what words do the sutras use?

Although 'impulsive' can describe a part of what exactly "akusala" means, I'm not sure if we can see it as an English translation of the Pali word "akusala".
As we know, "Akusala" is the antonym for "Kusala".
"Kusala kamma" denotes "Righteous action" or to simply put it, "Good/virtuous actions' ,which are actions that bring happiness and give rise to pleasant feelings. h
Hence, "Akusala" is just the exact opposite of this....that is it means something sinful or immoral, something that yields results that are unpleasant for one's heart.
I personally think, 'unrighteous' ,'unvirtuous' or something as simple as 'wicked' can be the closer translation of 'Akusala'.
Hope this helps :)

As I see it, impulsive is not the right word to describe “Akusala”.  Because the word is the opposite of “kusala”, depending on the situation and what I would have to convey, there are other ways to better describe it; for example:

If “kusala” denotes the advantageous, the “akusala” is disadvantageous when referring to intentions, as in  kusala and akusala-cetanā.
If “kusala” denotes the wholesome, the “akusala” is unwholesome when referring to the roots of the wholesome (kusala-mula) and the roots of the unwholesome (akusala-mula).
If “kusala” denotes the meritorious, the “akusala” is de-meritorious when again referring to volition (Kusala Akusala Cetana).

When “kusala” is the Good, the “akusala” is the Bad/Evil.
When “kusala” is the Advantageous, the “akusala” is the Disadvantageous / detrimental.
When “kusala” is the Skilful, the “akusala” is the Unskilful.
I can understand you wanting to define it as “impulsive”. But since the defilement tends to work impulsively, without deliberation, the transgression is less serious than slander and the kammic consequence generally less severe. Still, harsh speech is an unwholesome action with disagreeable results for oneself and others, both now and in the future, so it is a “akusala”.
I agree that we speak and we act impulsively, and out of our thoughts arise speech and action. It just means that mindfulness and clear comprehension were lacking.
Two suttas to read on “Akusala” are:

(Akusalamula) Aññatitthiya Sutta - A 3.68. The nature of the 3 unwholesome roots.
(Akusala) Kamma Nidana Sutta - A 10.174. The negative root causes of karma.

authors: Баян Купи-ка


text:
Which materials exist on the construction and origin of kōans?
A further question: is there an online community that creates kōans?
Thank you so much!
John

This book might be useful: The Koan. Texts and Contexts in Zen Buddhism. By Steven Heine e.a. With contributions from several specialists in the field

Thank you Franklin, I purchased a copy and it is very interesting.

A kōan is nothing more than a puzzle that seems self-contradictory or paradoxical, and yet contains a teaching of truth in it. Those who want a book about it are probably unqualified to create kōans to begin with.
That being said, each sangha (whether online or not) can adopt kōans as they see fit, whether validated by a group of masters or not. Such validation serves only to give a thorough review of the proposed kōan, and doesn't pertain to whether or not it validly teaches, since the acceptable answers can vary greatly between students and even teachers. The abstract quality of a kōan to begin with makes it an uncertain thing at best, anyway.
There is not any particular qualification, other than understanding what a kōan actually is, in its full and ineffable truth. Any book on the subject would necessarily have to ignore the ineffable (e.g., indefinable) part of that, and so would completely miss the point of the abstract. But if it was to teach you what you need to get to the level of abstract comprehension, that would suffice, and there are lots of those.

Thanks for your thoughts Vishwa. My question was intended literally - your answer suggests you haven't encountered a text along those lines. I have sought out and ruminated on koans for many years. What I am driving at with this thread is something else - the (experiential) origin and (linguistic) creation and mechanics of koans, not their power over consciousness (which I have no interest in quantifying). What you termed "ineffable" is the effect, I am interested in how the language operates. Hard to describe :)

I think you'd have a very difficult time disentangling the linguistic creation of koans from their power over consciousness e.g. the psychological impact of Joshu's cypress tree vs. a maple tree for instance.  That said, your comment would make for a very interesting question.  I'm just not sure there's anyone around who could answer it!  :)

You know the definition of "kōan" is "case," right? As in "law case" for instance; or as in "the case of the purple pimpernel." Maybe because Zen did not have the large body of writings that Indian Buddhism had, examples were used as a teaching method. After a while the best - maybe most profound - examples were collected, as in the Blue Cliff Record. There was never a secret to constructing them, they are each a record of an instance that happened.

I don't know of any book on the history and development of koans, but I'm sure one exists if you care to search. Many collections have some background information in the introduction, and the individual commentaries often include background information. Further discussion of koans is scattered throughout Zen texts in general.
A koan is a koan because it makes an important point about practice and has been used for teaching for a long time, so it's debateable whether or not it's possible to create new ones. There's over a thousand traditional koans in existence, so there's no shortage :)


text:
Cyclical time in Buddhism
I've been learning about time and the varyous perspectives that it is viewed through, and it seems like there are two main ways of thought. The first, generally associated as a western mindset, is that time is linear. The second, and this is generally considered more eastern, is that time is considered cyclical. I'm pretty sure that this is also a common way-of-thought in Hunduism, but I'm, in particular, wanting to learn more about the nature of time from a buddhist perspective. Of what I have read sutra-wise (pretty much just the Lotus Sutra), I have only seen time's cyclality being alluded to once, when Shakyamuni Buddha is saying that, at the end of a kalpa, when the world is consumed by fire, his pure land will, although appearing to burn with the rest of the world, stay safe and untouched. I assume from this that at the end of kalpas, it was considered that the world would burn (maybe signifying the start of a new cycle). Anyhow, I'm just wanting to know more about the nuances of Buddhist-cyclical time and how one can comprehend/view the world in such a way.

Cyclicality and Linearity are both alluded to in Buddhism. Essentially many beings are trapped in Samsara living their lives and doing similar things over and over through the aeons because they are chasing after the same endless desires and suffering the same afflictions. However, it is also linear in the fact that progress is possible, you can transcends Samsara by practicing the Noble Eightfold Path. The future is by no means fixed that you are required to repeat the past. The world have many internal cycles but it is also moving forward. You can see day turn into night into day, and each day we do many similar things we have already done before, but it is also not quite the same day, and you will certainly be a different person 10 years from now.
The ultimate goal of Mahayana Buddhism is to liberate all beings, turning the world into a Pure Land of peace and joy. Yes, such a goal is very distant but never the less they strive towards that goal.

There is the cyclical nature of life in Samsara. The doctrine of Paticcasamuppāda (Pāli) states that when certain conditions are present, they give rise to subsequent conditions, which in turn give rise to other conditions. This is the cyclical nature of life in Samsara. If you read the Mā Puñña Bhāyī Sutta – It.22 it can be said that even time is cyclical.
Buddha had the ability to see the past up to infinite time such as many Sanvatta Kalpa, Vivatta Kalpa, and Sanvatta Vivatta Kalpa. Sanvatta kalpa means the time that takes the world to be destroyed after countless years. Vivatta kalpa means, time of the beginning of the world. In the Mā Puñña Bhāyī Sutta – It.22, Buddha says that:

…when it was the time of the world’s destruction, He was born in the Ābassara divine world. And when it was the time of the beginning of the world, He was born in a beings-free Brahma abode as a Brahma divine being. The Buddha also said that He was born as the Mahā Brahma in the Brahma realm for seven times and as the Sakkra who is the head of all deities in Cātum Māhārājika and Thāvatinsa divine worlds for thirty six times.


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The healing Bodhi tree for Shakyamuni Buddhas long term sitting?
Recently I heard from a group of commentators that the Bodhi tree, a tree species which Buddha choose to attain enlightenment under, was actually known to have medicinal properties. Has anyone ever heard this before? Apparently, this tree was what allowed Buddha to sit under the tree for long periods of time without developing pressure sores across his lower body. This particular sect of Buddhism believes Buddha sat under the tree for at least 7 years. Honestly I'm not surprised to find apologetical statements because of their position. Does anyone know if the Bodhi tree actually has these "medicinal" properties? Also, would you consider it's properties sufficient enough in explaining away the lack of pressure wounds we would expect to find on Buddha's body?
To summarize my question:

Does the Bodhi tree actually have medicinal properties as some Buddhists claim?
Are the medicinal properties sufficient enough in explaining away the pressure sores we would expect to find on Shakyamuni's body through his prolonged meditation model (years)?
Please no short term models to undermine the question, thank you.

Does the Bodhi tree actually have medicinal properties as some Buddhists claim?
Maybe it does? For example, Phytopharmacology of Ficus religiosa references studies which say it does. I can't judge whether these are good/reliable studies (questioning the reliability of those studies might be a good question for Skeptics.SE if you really want to pursue it).

Are the medicinal properties sufficient enough in explaining away the pressure sores we would expect to find on Shakyamuni's body through his prolonged meditation model (years)?
I can't say I'm an expert on pressure sores, I'm not sure what to expect.
Bicyclists for example can sit on their saddle for hours and days on end, partly because they have become physically accustomed to it through practice/use.
Also, for what it's worth and for example, to prevent pressure sores in a bed-ridden geriatric patient, this paper says,

When older adults are admitted to a hospital or a nursing home, caregivers should inquire how often patients will be repositioned, Edsberg says. She suggests ascertaining the facility’s policy on repositioning. “It’s recommended that the patient be repositioned every two hours,” she says. “Caregivers might want to consider being proactive in enforcing this by setting a timer in the patient’s room so that it’s not forgotten.”

It also recommends good nutrition. Anyway, that confirms my preconception that occasional repositioning is important (and is used) to help prevent pressure sores.
See also this topic, Buddha meditation under the bodhi tree, which questions whether the Buddha "sat and did not move for days"... a meditator might change position occasionally.
Also I presume that Gautama maybe did develop sores and so on, when he was practicing during his ascetic period.

I suppose that ideally to answer this question you might like a comparative (double-blind) study of people sitting on Bodhi tree leaves, or something like that (I don't know of such a study); or an answer from someone with personal experience of it.

The Bodhi-Tree is sacred to Buddhists. In the scriptures it says that Ven. Ananda once asked the Buddha what could be done to help the many disappointed devotees who travelled to Savatthi (a city of ancient India and one of the six largest cities in India during Gautama Buddha's lifetime)  to see the Buddha, only to find that He was away attending to another in distress. The Buddha then advised Ven. Ananda to plant a sapling from the great Bodhi tree under which He had attained enlightenment in Savatthi. It was at this occasion that He proclaimed that the Bodhi Tree would be a symbol of the Buddha that devotees could venerate in His absence.
I have not heard of any healing/medicinal properties but even to this date we can see devotees conducting Bodhi Poojas at the local temples to invoke blessings. What is important IMO, is to get a true understanding of the Dhamma than having a belief that all problems could be solved by Bodhi Poojas.


text:
Separating meditation into vipāssana or samatha
Did the Buddha teach a single meditation that includes jhāna and insight, or do the scriptures have him separate meditation into different techniques? In what Buddhist traditions is it necessary to qualify meditation as vipāssana or samatha?

It is said in the scriptures that depending on the type of person, that person falls into the PATH in four different ways. That happens through insight (vipassana) and tranquillity (samatha). If a person listens to true Dhamma, take part in Dhamma discussions, and practise Samatha and Vipassana properly, dispassionateness with understanding definitely take place in him/her. That’s a given. If not so, then the fault is in that person. It is because of doing something which appears as correct thinking, or erroneously thinking that what one does is the correct thing. That is where the mistake is and not in the Suttas or in the Noble Eight-fold Path.
In the Yuganaddha Sutta (Anguttara Nikaya Sutta 4.170), it is said that insight (vipassana) and tranquillity (samatha) is developed in Tandem. In this sutta, Ven. Ananda describes the paths to arahantship by which insight (vipassana) and tranquillity (samatha) work hand-in-hand.
There are people in whom the other three ways may work. These three are:
Samatha followed by vipassana - after which the path is born in him/her;
Vipassana followed by samatha - after which the path is born in him/her; &
The mind stays fixed internally and become one-pointed - after which the path is born in him/her.

so to clarify, the Buddha did not teach meditation by separating it into e.g. "go do vipāssana", but rather the scriptures tell us that vipassana is a quality of mind and an attitude to approaching meditation.

In an earlier post I wrote a bit more on the above point. If you get to read the Dantabhūmi Sutta (MN 125)  it says that the body, or parts of the body, such as out-breath and in-breath resemble the post in the stockade to which the elephant is tied. Kayagati-sati resembles the rope by which the wild elephant is tied to the post. The preparatory work towards samatha and vipassana resembles the preparatory training of the elephant. The work of samatha and vipassana resembles the parade ground or battlefield of the king.

'Samatha' means 'tranquility' while 'jhana' is a certain degree of 'mental collectedness' ('samadhi' - 'concentration'). 'Samadhi' & 'samatha' are not synonyms.
For the most part, the suttas teach samatha (tranquility) & vipassana (insight) are developed in tandem (MN 149).

Thus for him, having thus developed the noble eightfold path...for him these two qualities occur in tandem: tranquility & insight.

Both samatha ('pleasant abiding') & vipassana ('focused on arising & falling') are fruits of concentration (AN 4.41).
In the Anapansati Sutta, each of the sixteen lessons (apart from the 1st two) has the words: "He trains himself", which means training ('sikkha') the mind in higher morality, higher concentration & higher wisdom. Therefore, vipassana occurs in the successful practise of each of these 14 lessons (as well as samatha in lessons 4, 8, 10, 11, 12, 14 & 15). For example, to concentrate on the breath will result in the breath calming (which is samatha; lesson 4) but will also result in seeing clearly the breath is impermanent & that the quality of the breath conditions/affects the quality of the body & mind (which is vipassana; lessons 3 & 4).

Wow thanks again !

Are you saying that samatha and vipassana follow chronologically from the development of samadhi?

Yes....  samatha and vipassana follow chronologically from the development of samadhi


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How to improve mindfulness of thinking?
Recently I've been facing problems with trying to remain mindful of any thoughts that pass through my mind. This problem is particularly prevalent in my formal meditation, where I only realise I am thinking half way through the thought, or even when it has stopped. I also cannot remember the first parts of the thought pattern, what made it to arise, etc. Any tips on keeping a more stable eye on this 'frame of reference'? Thanks.

Hello and welcome to Buddhism SE. We also have a Help Center with useful resources. Enjoy your time here.

My understanding is the 3rd frame of reference (cittanupassana) does not involve observing thoughts (vitakka). It involves knowing whether the mind-heart (citta) is defiled or not. Defilements (kilesa) are not thoughts. Although there can be 'defiled thoughts', 'defilements' (kilesa) are the energy/drive/mood of greed, hatred & delusion, which are not thoughts.
For example, when there is sexual lust, anger or fear, the energy or vibrations that runs through & simulates the physical body with lust, anger or fear, giving rise to all kinds of physical reactions & tensions, is not 'thought'.
The teaching about the 3rd frame of reference does not mention thoughts. It states:

And how does a monk remain focused on the mind in & of itself? There is the case where a monk, when the mind has lust, discerns that the
mind has lust. When the mind is without lust, he discerns that
the mind is without lust. When the mind has hatred, he discerns
that the mind has hatred. When the mind is without hatred, he
discerns that the mind is without hatred. When the mind has
delusion, he discerns that the mind has delusion. When the mind is
without delusion, he discerns that the mind is without delusion.
When the mind is constricted, he discerns that the mind is constricted. When the mind is scattered, he discerns that the mind is
scattered. When the mind is enlarged, he discerns that the mind is
enlarged. When the mind is not enlarged, he discerns that the mind is
not enlarged. When the mind is surpassed, he discerns that the mind is
surpassed. When the mind is unsurpassed, he discerns that the mind is
unsurpassed. When the mind is concentrated, he discerns that the mind
is concentrated. When the mind is not concentrated, he discerns that
the mind is not concentrated. When the mind is released, he discerns
that the mind is released. When the mind is not released, he discerns
that the mind is not released.
Satipatthana Sutta

To be able to observe clearly or meticulously the arising, existing & passing of thoughts requires a high degree of concentration (mental collectedness/clarity/stability). The teachings state:

And what is the (mental) development using concentration (samādhi) that, when developed & pursued, leads to mindfulness (sati) &
clear-comprehension (sampajaññā)? There is the case where feelings
(vedanā) are known to the monk as they arise, known as they persist,
known as they subside. Perceptions (saññā) are known to him as they
arise, known as they persist, known as they subside. Thoughts
(vitakkā) are known to him as they arise, known as they persist,
known as they subside. This is the (mental) development using
concentration that, when developed & pursued, leads to mindfulness &
clear-comprehension.
Samadhi Sutta

A tip I can provide is to develop concentration (samadhi), such as by using Mindfulness With Breathing (Anapanasati).
An analogy is as follows. If you wish to scientifically examine water, ideally, you take a drop of water & place it under a microscope. You do not walk into a raging surf (in the ocean) with a microscope. Similarly, to observe thoughts in a meticulous manner generally requires a large amount of concentration and a small amount of thoughts.

I don't think this is a sign of weak mindfulness. Actually, the opposite might be the case: When your mindfulness improves you'll be able to see more clearly. But seeing more cleary often means seeing the mess and chaos in mind and body that is going on all the time whether we are aware of it or not.
Moreover, you're describing the 3 characteristics:

Thoughts are impermanent and change quickly
You cannot control when a thought comes up, nor can you really control your awareness of thoughts
Thoughts are not satisfying. You say not being aware of thinking is a problem for you. Who was first, the thought or you not being a aware? (Not) wanting and therefore suffering can arise from thoughts.

I wouldn't worry about it too much. Wherever you catch thinking that's where you should note it. If you realize you were not mindful you can note it with 'knowing'. Actually when you realize you were not mindful before, that's the only way of becoming mindful again, by becoming mindful of not being mindful.
But having a stable eye is really a wrong perception of what meditation is about. It's supposed to be unstable.

This is an interesting take on it; actually, a few months ago, I was quite good at tracking at least the first thought in a chain of papanca thinking. It was still a retrospective sort of remembrance, but I remember that I was doing it at the start of a dream, and how I managed to get to this story:) But it had an unhelpful tint: I would anticipate thoughts, in an anxious sense of aversion to them.

I'd honestly say to focus on your breath, then just allow thought to come and go naturally.
If you have trouble "noting" your thoughts or thought process--try instead to focus on the feeling that the thought produces.
Remember though, the idea of noting thoughts is one of a very soft touch, never forcing yourself to think about your thinking.  Quite simply acknowledging that a thought exists or has passed is more than enough.
Everything else depends on time and practice.  And try not to try so hard. :)

Sorry had deleted my comment. Great info in @Dhammadhatu answer including some Buddhist passages to look into. Much of my training has been very practical and less dogmatic, so really cool to read some of this. Ultimately, both answers provide nearly the same insight in different ways.  :)

I agree our answers are similar. Thank you for your comment & welcome.

THE 18 INVESTIGATIONS. 'Bhikshu, this person is made up of the eighteen mental investigations';
so it is said. And in what connection is this said?
i. On seeing a form with the eye,
   one investigates the form that is the basis for mental joy,
   one investigates the form that is the basis of mental pain,
   one investigates the form that is the basis of equanimity.
ii. On hearing a sound with the ear,
   one investigates the sound that is the basis for mental joy,
   one investigates the sound that is the basis of mental pain,
   one investigates the sound that the basis of equanimity.
iii. On smelling a smell with the nose,
   one investigates the smell that is the basis for mental joy,
   one investigates the smell that is the basis of mental pain,
   one investigates the smell that is the basis of equanimity.
iv. On tasting a taste with the tongue,
   one investigates the taste that is the basis for mental joy,
   one investigates the taste that is the basis of mental pain,
   one investigates the taste that is the basis of equanimity.
v. On feeling a touch with the body,
   one investigates the touch that is the basis for mental joy,
   one investigates the touch that is the basis of mental pain,
   one investigates the touch that is the basis of equanimity.
vi. On cognizing a mind-object with the mind,
   one investigates the mind-object that the basis of mental joy,
   one investigates the mind-object that is the basis of mental pain,
   one investigates the mind-object that is the basis of equanimity.
'Bhikshu, this person is made up of the eighteen mental investigations': so it is said in this connection.

Dhātu Vibhaṅga Sutta similarly in Titth’ayatana Sutta
Essentially there are 3 sensation which arise due to metal activity: pleasant, unpleasant and neutral which gives arise to the unwholesome roots. It is by looking at these sensations with equanimity and rightly seeing their impermanence you can prevent them from arising. [Pahāna Sutta, Avijja Pahana Sutta 2]
Being mindful when thinking you should not have the unwholesome roots to arise. If it does this leads to unwholesome action, hence unpleasant results in the future. [Mula Sutta] If your thinking is without the unwholesome roots then there is no future unpleasant results. This is what you should aim for in being mindful while you are thinking, i.e., do not let the unwholesome roots arise, do not let the hindrances arise, do not let the Vipallasa arise. This can be achieved by being equanimous and watching the arising and passing of phenomena. Having Wise Attention all 8 Path Factors develop automatically. [Yoniso Manasikāra Sampadā Sutta]


text:
Can anyone identify which suttas these quotes (having to do with the sense of self) come from?
This document contains instructions for ridding the sense of a personal self. I was wondering which suttas (or other texts) the quotes at the end come from:

“By rightly understanding ‘I am,’ one makes and end of suffering.”

and:

“The eradication of ‘I am’ is the attainment of Nibbana here and now.”

I think the first one is for example the Kutuhalasala Sutta (SN 44.9) (S iv 398), the relevent sentence in that translation being:

Instead, he describes him thus:

"He has cut through craving, severed the fetter, and by rightly breaking through conceit has made an end of suffering & stress."'

I think that "rightly breaking through conceit" might be a translation of of the same text as "rightly understanding ‘I am’" (because "breaking through" = "understanding", and "I am" = "conceit").
There's more about the relationship between "conceit" and "identity view" in the answers to this topic.
Another translation is here:

But, he declares of him, thus:

“He has cut off craving, and through full mastery over conceit, he has
    made a total end of suffering.”

This gives the Pali in a footnote:

Acchejji taṇhaṁ vivattayi saññojanaṁ sammā,mānâbhisamayā antam akāsi dukkhassâ ti.

Here's part of a dictionary definition of one of those words, Abhisamaya

Abhisamaya, (abhi + samaya, from sam + i, cp. abhisameti & sameti; BSk. abhisamaya, e. g. Divy 200, 654) “coming by completely”, insight into, comprehension, realization, clear understanding, grasp, penetration.

So you can see how that word might be translated as "understanding" and/or "penetration".
A later part of that same dictionary definition says,

sammā-mān’âbhisamaya full understanding of false pride in ster. phrase "acchecchi (for acchejji) taṇhaṃ, vivattayi saññojanaṃ sammāmānâbhisamayā antam akāsi dukkhassa" at S.IV, 205, 207, 399; A.III, 246, 444; It.47

... in other words:

It's a "ster. phrase" (maybe "stereotypical phrase"?)
That dictionary translates it as "full understanding of false pride"
It can be found in several suttas, including S.IV (205, 207, and 399), A.III (246 and 444), and It.47.

And indeed, as stated in that definition, here it is again at the end of (for example) the Nissaraniya Sutta (AN 5.200) (A iii 245):

He has cut through craving, has turned away from the fetter, and by rightly breaking through conceit he has put an end to suffering & stress.

So it's found in at least two of the suttas (quoted/hyperlinked above), and presumably found in at least all 6 of the suttas referenced in the dictionary definition above.

What I find interesting in the citations you provided is the emphasis placed on craving. It seems to classify 'breaking through conceit' as just one of the conditions for cessation of suffering. This is also in line with the severing of the ten fetters. Self-view (Pali: sakkāya-diṭṭhi) is but one of those fetters (and a lower one, at that). Different ways of skinning a cat...

Not "different ways"? The fact that there are ten fetters implies it's necessary to eradicate all of them, doesn't it? The document you linked to in your OP says "granted it may take a little more as well", which I understand as saying that although eradication of identity-view is necessary, it is not sufficient. "Craving" is in the Pali phrase quoted in this answer (see the word taṇha). It's mentioned in the 2nd and 3rd noble truths; as rāgo it is 3 of the 10 fetters. SN 51.15 says that the aim is to abandon desire.

A noble disciple of the Buddha – a Stream Entrant – having let go of the clinging to the personality belief (sakkayaditthi), has to start working towards uprooting its more subtle form, in ‘Attavada’. One cannot be a stream-enter-or  as long as he is in possession of the personality belief.   Attavada  is the very last hindrance, if eradicated will realize Nibbana.
In the Khemaka Sutta: About Khemaka, SN 22.89  it says:

Friends, even though a noble disciple has abandoned the five lower fetters, still, in relation to the five aggregates subject to clinging, there lingers in him a residual conceit ‘I am,’ a desire ‘I am,’ an underlying tendency ‘I am’ that has not yet been uprooted. Sometime later he dwells contemplating rise and fall in the five aggregates subject to clinging: ‘Such is form, such its origin, such its passing away; such is feeling … such is perception … such are volitional formations … such is consciousness, such its origin, such its passing away.’ As he dwells thus contemplating rise and fall in the five aggregates subject to clinging, the residual conceit ‘I am,’ the desire ‘I am,’ the underlying tendency ‘I am’ that had not yet been uprooted—this comes to be uprooted.

In the Dīghāvu Upāsaka Sutta, SN55.3 Buddha states:

"Therefore, Dighavu, when you are established in these four factors of stream entry, you should further develop six qualities conducive to clear knowing. Remain focused on inconstancy in all fabrications, percipient of stress in what is inconstant, percipient of not-self in what is stressful, percipient of abandoning, percipient of dispassion, percipient of cessation. That's how you should train yourself." ….. Dīghāvu later passes away and arises spontaneously in the Suddhāvāsa as a non-returner.

Read Also Upasena Sutta: Upasena, SN 35.69.

Records the incident of the death of Upasena Vangantaputta from a snake-bite. Summoned by him, Sāriputta looked at him and said that he noticed no change at all in Upasena, either in his body or in his faculties. Upasena answered that that was because he had long before quelled all lurking tendencies of "I" and "mine."


text:
Sensory Deprivation tank
Have you heard of sensory deprivation tanks? This is a tank which is supposed to be soundproofed and dark, and which would hold a little water for a person to float in. The idea is for the conditions inside the tank to allow a person to enter a place where they can avoid all bodily sensation. Still not for creating aversion to the body/bodily sensations, is this type of experience valuable in the practice of meditation? Would you yourself consider trying this experience for yourself?

Hello Dylan and welcome to Buddhism SE. We also have a Help Center with useful resources for new comers that you might like. Enjoy your time here.

Sure. Meditation is a mental activity which means it can be done anywhere at anytime. It doesn't matter if you're on a bus, in your room, or in a deprivation tank.
So is a deprivation tank valuable? Sure! People today and in ancient times have always used sensory deprivation techniques to further their mind. Today, people still use ancient forms of sensory deprivation techniques such as retreats into caves, living in dark rooms, living underground to avoid sound and light, sitting in one place for a pro-long length of time, etc... The only downfall for deprivation tanks is that you can't live inside them. Otherwise, I could see it being beneficial. Though long-term sensory deprivation techniques should NOT be used by beginner practitioners. Your mind will begin to hallucinate after 2 - 3 days of continues deprivation. If you're not trained to handle the mind under these conditions it can be scary, strange, and confusing if you're not prepared to face it. The only kind of teachers I would trust in doing such an extreme meditation practice (myself being a zen practitioner) would be the  Buddhist Lama's living in Tibet. They are very intelligent, hard-core, and specialize in matters concerning the subconscious mind.
Here is a video of a group of men and women Hallucinating after a few days of visual sensory deprivation.


text:
Does Buddhism claim that our World is an illusion? In other words is it a Matrix? Any proof for this?
I wrote this article: Do people leave in Matrix? Information, entropy, time and cellular-automata.
The article tries to prove that the visible world is an illusion or a "dream".
My question here is, is "the visible world is an illusion or dream" the main topic of Buddhism?
Also, the article includes a proof of the existence of a Higher Conscience. Is that in direct relation with Buddhism (i.e. the topics discussed here on this site)?
Also, if you found any logical flaws in this article then please mention/list them.

The title asks a question, but the body-text does not. The body-text is a copy of this paper which is not a question about Buddhism. So, as currently phrased (i.e. in its current format), this doesn't seem to be a question about Buddhism. Why did you post that paper: are you asking for a critique of it? It seems to me to have so many logical flaws that they cannot all be addressed in this format (and addressing them isn't on-topic for this site).

hello ChrisW, there is an obvious connection with Buddhism. The article tries to prove that the visible world is an illusion or a "dream". Is that the main topic of Buddhism? Also, the proof of Higher Conscience existence is given. Is it a direct relation with the topics discussed here? If you found any logical flaw please mention. I put the article here for discussion and the questions stated in the article Title. I put the article here because i read in Buddhism section of this site - share your research. And, if you have nothing to comment and did not read anything please donot be negative

hello ChrisW, you claim there are logical flaws. i would like to hear at least one. do not be harsh as it is usually in forums. Buddhism section is promoting research, so here it is. If there is a logical flaw, please list it.

IMO the paper did not ask questions and is not about Buddhism, and therefore it wasn't a suitable 'question' for this site. I have edited the question (above) to include the actual questions, which you asked in your comments above. Is this OK with you, shall I reopen the question in this format, are these the questions which you want to ask?

Also the paper doesn't include the words "illusion" or "dream" anywhere; so I don't see why you claim in your question that, The article tries to prove that the visible world is an illusion or a "dream" ... your question might seem to be just about on-topic now, but its connection with the article (and the connection between the article and Buddhism) is tenuous.

Hello ChrisW, thank you that your reformulated it this way. the original article is mine actually. i just used a different name. i guess not everyone uses real name in forums.

Thank you. FYI all Stack Exchange sites including this one are Q+A ("question and answer") sites: they're designed for "Q+A", and not for "discussion". Their format is that each page/topic starts with a question, and other users post answers which reply to or address the question. For that kind of reason it's important that topics start with an specific/explicit question (and are not just a copy of or link to an article to be reviewed/discussed). The body text of the question should explain/define as clearly as possible what your question is; and the title should be a summary of that question.

My standard answer is: "It is a hologram of light with no screen or projector."

"My question here is, is "the visible world is an illusion or dream" the main topic of Buddhism?"
No, it's not the main topic of Buddhism.
From the Pali canon point of view, it's also not a claim of Buddhism that the world is an illusion.
In contrast, the main topics of Buddhism are the nature of suffering, the nature of pleasure, the ultimate freedom of suffering, and the ultimate pleasure (born from the freedom of suffering).
It's visible from the sutras that the Buddha refrained himself from making many ontological statements -- statements about "what is out there" and the nature of "what is out there". And some people seem to believe he refrained from making any ontological statements at all, which may induce the idea that he regarded the world as an illusion.
In general, however, his concerns with the world starts when a stimulus is "perceived" -- when sense data is contacted. The nature or reality of what lies behind what has been sensed is not dwelled on. Thus, generally speaking, the formulations of the World from the Buddha are in terms of the senses.

At Savatthī. “Bhikkhus, I will teach you the origin and the passing away of the world. Listen to that and attend closely, I will speak.”
“Yes, venerable sir,” the bhikkhus replied. The Blessed One said this:
“And what, bhikkhus, is the origin of the world? In dependence on the eye and forms, eye-consciousness arises. The meeting of the three is contact. With contact as condition, feeling comes to be; with feeling as condition, craving; with craving as condition, clinging; with clinging as condition, existence; with existence as condition, birth; with birth as condition, aging-and-death, sorrow, lamentation, pain, displeasure, and despair come to be. This, bhikkhus, is the origin of the world.
[...]
“And what, bhikkhus, is the passing away of the world? In dependence on the eye and forms, eye-consciousness arises. The meeting of the three is contact. [...]
-- SN 12.44

When he doesn't ignore "the outside world", it's possible that he could be speaking in conventional terms instead of positing a view, as in "there's a house behind that mountain" (and not as in "that house exists and it's real", in the ontological sense). When he speaks of characteristics of "the house", his focus arguably lies in what is perceived by the senses and his interest is in how these perceptions affect us.
The closer he gets to an ontological view (i.e. when the nature of the "house" is of interest) could still not really be about trying to pinpoint the actual nature of the thing "out there" independent of observer, but about the perception of it, in particular, associated with three characteristics: being subject to change, it's unsatisfactoriness as ultimate protection of all suffering and, upon inspection, showing a lack of ultimate stable essence.
On the other hand, he is known to have "proclaimed the world with it's devas, Mara and Brahma" against those who proclaimed otherwise, which is an assertion about "objective reality". Also, he taught a moral law which distinguish between sentient beings and non sentient beings which seem to imply some ontological distinction. But I think the interest to investigate the non-subjective actual nature of things is generally lacking when such knowledge does not benefit the path to terminate suffering.
Finally, since Buddhism regards mind as a sense (in the same category as taste and sight), then even in a universe where all interactions are confined within ones own mind, Buddhism still applies.

Why is this sutta not an ontological statement? Thanks http://www.accesstoinsight.org/tipitaka/an/an03/an03.134.than.html

@Dhammadhatu I think many syntactically apparent ontological statements (e.g. "all X is Y") in the suttas can be seen either way: it can be seen as actual ontological assertion qualifying the external thing independent of the observer or, for example, it can be seen as a "conventional" assertion about the perception of the external thing (where "is" really is just a shortcut for something longer such as "is perceived as", e.g. "all X is perceived as Y"). I think the latter fits nicely with the rest of the doctrine, and considering how conventional language issues are dealt within the canon

The sutta quoted is obviously not conventional language since it is about Dhamma Law. If the later fit nicely then enlightenment would be subjective or imputed by the observer. The sutta does not state that. The sutta states X = Y independent of any observers; independent of the arising of Buddhas. Conventional language in the Canon refers to worldly idioms such as "I", "you", etc. It does not apply to impermanence, not-self, etc. All language or description is not "convention". Refer to SN 5.10; SN 1.25; MN 98, etc

I don't mean "conventional" as just "sammuti sacca", i mean informal (in contrast to a formal statement in a logical system) therefore imprecise, ambiguous.  One could say "the ball is red" and take this as an ontological assertion declaring "red" to be a property of "ball", however "red" is a phenomenom created by the eye organ and vision system (e.g some people and animals see different colors according to their biology). So "red" is not a property of the ball, it's just perceived as "red", despite the syntactical form being accepted and obviously showing otherwise. Thus i have reservations.

Impermanence, not-self, etc, are not phenomenom created by the eye organ and vision system. Impermanence, not-self, etc, are properties of a ball,

In the Diamond Sutra the Buddhas says
“All conditioned things
are like dreams, illusions, bubbles, shadows
they are like dew or lightning
this is how they are to be viewed"
This is since all phenomena like the world are impermanent and therefore subject to an end like an illusion

Can you recommend (or link to, online) a specific translation of the Diamond Sutra?

Sorry I mostly read it in Chinese but I also read Master Xuan Hua's version in English which was pretty good        http://www.cttbusa.org/vajra/vajrasutra.asp

..is "the visible world is an illusion or dream" the main topic of Buddhism?...includes a proof of the existence of a Higher
Conscience...if you found any logical flaws...please mention/list
them...

In my fleeting personal illusory opinion, there is no obvious connection to Buddhism here at all.
In Buddhism, it is consciousness that is an illusion or dream, i.e., there is no higher consciousness in Buddhism. To quote from the Buddhist (Pali) scriptures:

Now suppose that a magician or magician's apprentice were to display a magic trick at a major intersection, and a man with good eyesight
were to see it, observe it & appropriately examine it. To him —
seeing it, observing it, & appropriately examining it — it would
appear empty, void, without substance: for what substance would there
be in a magic trick? In the same way, a monk sees, observes &
appropriately examines any consciousness that is past, future or
present; internal or external; blatant or subtle; common or sublime;
far or near. To him — seeing it, observing it, & appropriately
examining it — it would appear empty, void, without substance: for
what substance would there be in consciousness?
Phena Sutta

While it is difficult to argue using Buddhism, the quote below does lend support to a theory that the visible world is less an illusion than consciousness. For example, it would take a lot of arrogance or hubris to suggest Mt Everest, which has logically existed for millions of years, is an illusion, yet consciousness, which only lasts a short moment, is not an illusion but something "higher".

It would be better for the uninstructed run-of-the-mill person to hold to the body composed of the four great elements, rather than the
mind, as the self. Why is that? Because this body composed of the four
great elements is seen standing for a year, two years, three, four,
five, ten, twenty, thirty, forty, fifty, a hundred years or more. But
what's called 'mind,' 'intellect' or 'consciousness' by day and by
night arises as one thing and ceases as another. Just as a monkey,
swinging through a forest wilderness, grabs a branch. Letting go of
it, it grabs another branch. Letting go of that, it grabs another one.
Letting go of that, it grabs another one. In the same way, what's
called 'mind,' 'intellect' or 'consciousness' by day and by night
arises as one thing and ceases as another.
Assutavā Sutta

My impression is the questioner might find an answer that might suit their tastes on the Hinduism forum: https://hinduism.stackexchange.com/ since Hinduism might teach more inherently the external world is an illusion & the Higher or True Self is permanent.

But, hubris is so much fun...

the "fun" is the ego not willing to die 100%... "ego" clinging

Regarding how long something has existed, Robert M. Pirsig (Zen and the Art of Motorcycle Maintenance) said basically: can something have existed before it was known of? Did 2 + 2 = 4 "exist" before anyone cognized it? In what sense? Further, he said: did the fundamental laws of the universe, such as gravity, "exist" before the universe (supposedly) came in to being? This is perhaps the basis for people saying that there is only the present moment -- the moment of perception -- and thus no past or future. Stretching that, it is logical to say that everything is either illusory, or empty.

the pali suttas state consciousness depends on sense organs & sense objects (rather than sense objects depend on consciousness). this is the buddhist view. to believe consciousness is the creator of the universe is believing consciousness is god. this is brahmanism rather than buddhism. AN 3.134 states the laws of nature exist regardless of whether they are known. this is buddhism rather than popular novels

This is not the main topic of Buddhism. Such ideas are called 'speculative views'. I think a good reference would be MN 63.

"It's just as if a man were wounded with an arrow thickly smeared with poison. His friends & companions, kinsmen & relatives would provide him with a surgeon, and the man would say, 'I won't have this arrow removed until I know whether the man who wounded me was a noble warrior, a brahman, a merchant, or a worker.' He would say, 'I won't have this arrow removed until I know the given name & clan name of the man who wounded me...
"In the same way, if anyone were to say, 'I won't live the holy life under the Blessed One as long as he does not declare to me that 'The cosmos is eternal,' or 'The cosmos is not eternal,' or 'The cosmos is finite,' or 'The cosmos is infinite,' or 'The soul & the body are the same,' or 'The soul is one thing and the body another,' or 'After death a Tathagata exists,' or 'After death a Tathagata does not exist,' or 'After death a Tathagata both exists & does not exist,' or 'After death a Tathagata neither exists nor does not exist', the man would die and those things would still remain undeclared by the Tathagata.
"And why are they undeclared by me? Because they are not connected with the goal, are not fundamental to the holy life. They do not lead to disenchantment, dispassion, cessation, calming, direct knowledge, self-awakening, Unbinding. That's why they are undeclared by me.
"And what is declared by me? 'This is stress,' is declared by me. 'This is the origination of stress,' is declared by me. 'This is the cessation of stress,' is declared by me. 'This is the path of practice leading to the cessation of stress,' is declared by me. And why are they declared by me? Because they are connected with the goal, are fundamental to the holy life. They lead to disenchantment, dispassion, cessation, calming, direct knowledge, self-awakening, Unbinding. That's why they are declared by me.

Also referred to as "Thicket of Views" and "Vexing Questions".

My question here is, is "the visible world is an illusion or dream" the main topic of Buddhism?
I'm not sure. I think the main topics of Buddhism include, "What is good and not-good for people?", and "Why do we suffer or find things unsatisfactory? What can we do about death and illness and so on?"
I've heard "the world is an illusion" as a (uninformed?) summary or paraphrase of Buddhism, but I don't know where that summary comes from. That's not the message that I get when I read translations of the suttas.
The word I associate with "illusion" is Maya. Wikipedia's article on Maya (illusion) suggests that's not really a feature of Theravada Buddhism; and when it's used within Mahayana it's used in the context of "misunderstanding based on ignorance".
It is apparently a feature of Hinduism and other Indian philosophies. I guess that possibly that's where the impression that "Buddhism teaches that the world is illusion" comes from, i.e. maybe it comes from people being vague about the difference between Buddhism and other eastern philosophies (some views which are, IMO, vague and similar were also maybe popularized as a take on 'physics' e.g. in the 1970s -- see Quantum mysticism).
I won't say that the theory the "the world is an illusion" is useless, but my very limited (or non-existent) understanding of the theory is more-or-less useless to me: because (unlike the more useful scientific 'models') this theory is neither predictive (explaining/predicting what's going to happen), nor prescriptive (explaining/recommending what we should do about that).
It's possible that "illusion" is a poor translation of something which is a topic of Buddhism. One of Buddhism's themes is "ignorance" or avijjā. I think there are various forms of ignorance, especially "seeing impermanent things as permanent" or not properly considering that things are impermanent.
Buddhism distinguishes between so-called right and wrong views. 'Right view' is the right way to view things, wrong view is the wrong way. Right view is the "fore-runner" in the sense that it's because of (or conditioned by) having right or wrong view that we think and do right and wrong things (where "right" is the translation of an adjective Sammā which is e.g. described/defined here).
This summary of right view extracts definitions of 'right view' from various suttas. IMO this passage ...

And what is wrong view? 'There is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no brahmans or contemplatives who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.' This is wrong view...

... says more-or-less explicitly that disregarding or denying the existence of these things (e.g. regarding them as illusion) is 'wrong'.
To the extent that Buddhism does talk about illusion, I think that illusion consists of placing an improper value on something. If I hate something, if I fear it, or if I crave it, then it's important to me ... perhaps an undue importance, whereas it would be better if I were more equanimous towards it.
There's part of Buddhism teaching that's interested in, I don't know what you call it, 'phenomenology'? Maybe 'phenomenology', I don't know (I was never taught philosophy).
Buddhism is interested in how 'craving' comes to be (because 'craving' is identified as a or the cause of suffering). This Wikipedia article Ayatana is a summary of that: it says that 'craving' arises from 'feeling'; and that 'feeling' arises from 'contact' between three things, i.e. a 'sense-object' (e.g. "something seen"), a 'sense-organ' (e.g. "eye"), and 'sense-consciousness' (e.g. "sense-consciousness of sight").
Maybe it's important to be aware that what/all you crave (or used to crave) comes from senses in this way, and that these sense-impressions are transient or fleeting (impermanent). I think some Buddhist literature describes these fleeing sense-impressions (or moments of consciousness, or more specifically moments of contact between consciousness and senses) as "like foam" or like a soap bubble. Our consciousness of things is, what shall I say, unstable: e.g. it's one thing after another.
Anther kind of "illusion" is that there's a continuous "I". I think that Buddhism does not argue that the world is an illusion, rather that it's the "I" that's an illusion ... or if not an illusion, that "egoism" is "wrong" in the sense that having a sense of I results in a "thicket of views" and no end to suffering.
One of the most famous suttas (Anatta-lakkhana Sutta: The Discourse on the Not-self Characteristic) says,

Any kind of (form, feeling, perception, determination, and/or consciousness) whatever, whether past, future or presently arisen, whether gross or subtle, whether in oneself or external, whether inferior or superior, whether far or near must, with right understanding how it is, be regarded thus:

'This is not mine, this is not I, this is not my self.

Later Buddhist doctrines begin to emphasize that the world is empty (note, not 'illusory' but 'empty'), by which I think they mean, 'empty of self'. It's also emphasized that things don't have an 'independent' existence, i.e. they're caused by things (or they arise when the conditions for their arising are present), and dissolve when those conditions are no longer present.
Taking Dhammadhatu's example of Mount Everest I'd say it arises as a result of (or, 'is conditioned by') tectonic plate movement (and isn't or won't be eternal), and also that perception of it arises from causes (and is also impermanent).
In other words is it a Matrix?
Really? The capital M implies you're referring to the movie. I suppose I recommend this answer.
Any proof for this?
Any proof for what: proof for the world being illusion, or proof for what Buddhism teaches?
I find that part of what Buddhism teaches seems self-evident and/or common-sense, and/or it's a good description of already-observed phenomena (e.g. unhappy when a loved one dies).
It has also plausible theories (e.g. unhappiness may be caused by becoming emotionally attached to or expecting permanent happiness from something impermanent), which are also useful in the sense that they're prescriptive (e.g. to avoid unhappiness, you should avoid unwise attachment), with techniques and practices for doing that.
Also, the article includes a proof of the existence of a Higher Conscience. Is that in direct relation with Buddhism (i.e. the topics discussed here on this site)?
For reference, here is the article "proof of the existence of a Higher Conscience":

Definition: Higher Conscience is a conscience that has always more knowledge (amount of information) than all people have.
Theorem: Higher Conscience exists.
Proof: Assume that Higher Conscience does not exist. Then the number Pi can not exist in Human Conscience (knowledge of all people) since people know, describe and operate only with what they see or sense. But number Pi can be derived only from the fact that someone saw or sensed the circle (“perfect wheel”).

I think this is a fallacious proof: I think it's based on the assumption that the ability to reason about irrational numbers implies that there exists a "higher consciousness" which "knows" an infinite amount of information.
So far as I know that's nothing to do with Buddhism. FYI I think there are Early Indian treaties on mathematical infinities (but not especially Buddhist).
There are some supernormal abilities described in Buddhist literature: see e.g. Ṛddhi and Abhijñā, but I think consensus is that these aren't very important to the practice of Buddhism.
What is important to the practice of Buddhism is to eliminate or abandon mental stains such as greed and conceit.
Also, if you found any logical flaws in this article then please mention/list them.
I think that's off-topic for this site, but in case this helps ...

The paper proves that we leave in Matrix. We show that Matrix was built by the creator. By this we solve the question how everything is built

Just re. a spelling mistake, I think that "leave in Matrix" should be spelled "live in a 'Matrix'".
Anyway, IMO you don't "prove" those things: instead you state that you choose to describe or model the world in that way. However you don't IMO demonstrate that it's a good model. A good model would:

Account for many/all current observations
Make predictions about the future
Ideally make useful/testable predictions, be 'falsifiable'.

Then the number Pi can not exist in Human Conscience (knowledge of all people) since people know, describe and operate only with what they see or sense.

People (mathematicians) define Pi based on (some finite number of) axioms. For example a 'perfect circle' might be defined as 'a line whose points are equidistant from a centre', and that definition doesn't take infinite or 'higher' consciousness.
Mathematicians can also show that Pi is irrational/transcendental, and can't be expressed in finite decimal digits. I don't think they infer that there's an infinite matrix or Matrix which contains these digits.
It's a bit of a jump (too much of a jump) to say, "I can do geometry, therefore an infinite/random/evolving creator-God exists". I think that's mere conceit (attaching undue importance to one's ideas).
Incidentally I think that Buddhism sees ideas as being a kind of sixth sense, similar to the other five: e.g. in the same way that an "an eye perceives sights" you can say that "a mind perceives ideas".

Hence Infinite Monkey who typed EVERYTHING EXISTS

These basis of this argument seems to me to be:

The probability of randomly typing "banana" on a 50-key keyboard is ((1/50)6
Doing so would require infinite monkeys
I am a monkey, who has just typed the word "banana"
Therefore "infinite monkeys" exist

Some logical fallacies with this argument are:

"banana" is not a random word
although "I am a monkey" I don't type randomly

In summary you seem to be arguing that:

I observed something
It happened at random
Therefore every other possibility exists simultaneously

Theorem on Halting Problem

I think you're saying that an infinite problem could be solved with infinite computing resources; but you're using (fallacious) conclusions from previous proofs to assume that infinite computing resources exist.

Edit to add: see also this answer which says that the illusion/dream analogy comes from the Diamond Sutra, and that it's to be understood as emphasizing that phenomena (and/or perceptions of phenomena) are impermanent.

ChrisW, I wanted to receive real comments but got the logically incorrect answer, just endless speculations that are false. I think I made a mistake putting this in this forum.

Example, banana is not random word, yes, but my theorem investigates what is the probability to type or not to type word banana. you missed the point. the same is with the previous theorem. you can not deny the existence of number Pi, and it exists, was derived, in Human mind. if Higher mind never existed you would never get the knowledge about number Pi because you do not see perfect wheel. This is like ontological argument. You can not disprove it. See also the prove of God existence by Kurt Godel.

and I put to Buddhist forum because from my proof that Higher mind exists it follows that our world is an illusion, a dream of Higher mind. I thought sleeping Buddha in Bangkok is a symbol of this. I hope I can remove this whole stuff from here one day.

and just to make it more clear, I repeat a definition - Higher mind is a mind that knows more than all people at any given moment. so, denying such Higher mind you get a contradiction that number Pi is already known to people. because it is only higher mind could teach about its existence.

since no one ever touched or saw a perfect wheel someone has given a knowledge about it. this someone is Higher mind since it knew at that point more than all people together - it knew about the existence of number Pi and its relation to a circle - perfect wheel.

I hope I can remove this whole stuff from here one day. You can remove your name from all this stuff if you want to ... by changing your name, or by deleting your account: http://buddhism.stackexchange.com/help/deleting-account