text:
Is Buddhism a religion?
I want to know that what is Buddhism and is it a religion or just a philosophy or a exercise ?
I really want to know more about it , is there a book about learning Buddhism?

Depending on the practitioner it can be a religion, a philosohpy or exercise.

Buddhism is a middle path to live life happily and overcome sorrows or how to prevent sorrows. Buddhism is a only religion which is based on philosophy and science. Buddhism is liberal, equality, humanity.

I find that Buddhism is not a religion, philosophy or science because it has nothing to do with a creator being, nor such in faith, it analyzes ultimate reality rather than conventional like philosophers, and it goes beyond science, combining the empirical with the unempirical, or the mind, which science is only beginning to assess and understand.

I would say Buddhism is a religion based on this definition of "religion" from the Merriam-Webster dictionary:

a personal set or institutionalized system of religious attitudes,
  beliefs, and practices

Buddhism also meets this dictionary.com definition of "religion":

a specific fundamental set of beliefs and practices generally agreed
  upon by a number of persons or sects

Buddhism is not a religion based on the definitions of "religion" that depend on God, supernatural power, faith in God or worship.
A classic book for a beginner to read is "What the Buddha Taught" by Walpola Rahula, which can be downloaded here.
Two good beginner articles to read are The Buddha and His Dhamma by Bhikkhu Bodhi and An Introduction to the Buddha, Dhamma, & Sangha by Thanissaro Bhikkhu.

The first definition is circular, using the word it's defining in the definition!

The supernatural power appears in every Nikaya's Vinaya, not only Theravada? >>> Buddhism is not a religion based on the definitions of "religion" that depend on  supernatural power.

The Buddha did not ask for anyone to take his word with respect to Dhamma - things as they are. He asked people to not blindly obey, to not follow ritual, to not ignore or go against what they directly observe. In this respect, Buddhism is at its core a scientific method.
The Buddha's primary insight was acknowledging that all observed phenomena are conditioned and impermanent. This is not a speculation, but an observation. The reasoning then goes through the logical inference of dukkha (unsatisfactoriness, stress/suffering - impermanent things cannot be permanently satisfactory), bringing around the doctrine of non-Self, anatta - which does requires faith in that the direct observation of this truth is only available upon enlightenment, or the ceasing of mental fermentations.
The Kalama Sutta and MN27 offer direct evidence that the Buddha's message was closer to a scientific method than a religion, though one with a soteriological goal.

"So, as I said, Kalamas: 'Don't go by reports, by legends, by
  traditions, by scripture, by logical conjecture, by inference, by
  analogies, by agreement through pondering views, by probability, or by
  the thought, "This contemplative is our teacher." When you know for
  yourselves that, "These qualities are unskillful; these qualities are
  blameworthy; these qualities are criticized by the wise; these
  qualities, when adopted & carried out, lead to harm & to suffering" —
  then you should abandon them.'

(the above does still feature the wise, but not as absolute arbiters of right or wrong actions - that arbiter is solely the individual living his own practice, the wise offer previously gained experience, and are more accurately guides)
The similarities or differences between the modern scientific method and religions in general is what sources they accept for stated truths. Pramanas are a helpful guide for Hindu religions, but can be extrapolated to the Judeo-Christian world a bit.
Most major religions accept testimony of the wise, seers, prophets etc as truths, as well as others from the above link. Buddhism does not. Aside from direct perception as in MN27, inference is used in a limited way - as above when going from impermanence to non-Self, an inferred knowledge is gained about the nature of 'things', but this is not directly observed until nibbana, and inferred truths are not given any great weight within the scriptures. In addition, inferred truths can only arise from individually observed principles, so they rest on a base that is less prone to doubt than inferred truths resting on the base of prophetic statements etc.
Faith is required by a person who reads the Dhamma with respect to impermanence, if they at first disagree with it, and later non-Self, because gaining direct insight into this truth takes much more time and practice. Faith, so long as it starts from a verifiable base, is not by definition religious.
If you want the spiritual side, go to the source and read the Pali canon or Agamas (Chinese line), these are the closest you will get to the Buddha's direct words. There is philosophy, to the limit that it is a useful tool for gaining insight into things as they are, more often though it offers more practical lessons helping one aim for pacification of mind.
If you want the philosophy first, read Mulamadhyamakakarika - it is the culmination of Buddhist philosophical analysis. This is written 600-700 years after the Buddha, so is a more rigorous analysis of the above canon's statements on anatta.
It is, of course, possible to elevate Dhamma, 'things as they are', into a religion, and layties that have accepted Buddhism have often merged their cultural identities with the Buddha's message. But, to quote MN22, which sums up the process:

“And how is the bhikkhu a noble one whose banner is lowered, whose
  burden is lowered, who is unfettered? Here a bhikkhu has abandoned the
  conceit ‘I am,’ has cut it off at the root …so that it is no longer
  subject to future arising. That is how the bhikkhu is a noble one
  whose banner is lowered, whose burden is lowered, who is unfettered.
“Bhikkhus, when the gods with Indra, with Brahmā and with Pajāpati
  seek a bhikkhu who is thus liberated in mind, they do not find
  anything of which they could say: ‘The consciousness of one thus gone
  is supported by this.’ Why is that? One thus gone, I say, is
  untraceable here and now.
“So saying, bhikkhus, so
  proclaiming, I have been baselessly, vainly, falsely, and wrongly
  misrepresented by some recluses and brahmins thus: ‘The recluse Gotama
  is one who leads astray; he teaches the annihilation, the destruction,
  the extermination of an existing being.’ As I am not, as I do not
  proclaim, so have I been baselessly, vainly, falsely, and wrongly
  misrepres ented by some recluses and brahmins thus: ‘The recluse
  Gotama is one who leads astray; he teaches the annihilation, the
  destruction, the extermination of an existing being.’
“Bhikkhus, both formerly and now what I teach is suffering and the
  cessation of suffering. If others abuse, revile, scold, and harass the
  Tathāgata for that, the Tathāgata on that account feels no annoyance,
  bitterness, or dejection of the heart. And if others honour, respect,
  revere, and venerate the Tathāgata for that, the Tathāgata on that
  account feels no delight, joy, or elation of the heart. If others
  honour, respect, revere, and venerate the Tathāgata for that, the
  Tathāgata on that account thinks thus: ‘They perform such services as
  these for me in regard to this which earlier was fully understood.’

Religion - more broadly, any ideology - in my mind, ask for blind faith. The Buddha's message was only about dukkha and how be free of it. His method requires each individual to follow their own path, with an observer verifiable rationale behind it - blind faith never features.

Well this isn't true many suttas say to have faith and respect the dhamma the Kalama Sutta is often taken out of context since Kalamas were non-Buddhists.
"There are five detrimental things that lead to the decline and disappearance of the true teaching. What five? It’s when the monks, nuns, laymen, and laywomen lack respect and reverence for the Teacher, the teaching, the Saṅgha, the training, and immersion. These five detrimental things lead to the decline and disappearance of the true teaching." (SN 16.13)

Originally Buddhism is not a religion. Only in the past few hundred years that Buddhism gradually becomes a religion. If we could break from the notions of superstitions, we could actually benefit a lot from learning the teachings of the Buddha, that the principle of Buddhism is to help all beings to resolve delusions to attain happiness and enlightenment, to eliminate suffering, to gain serenity and purity of mind.
Buddhism is the most virtuous and perfect education directed by Buddha Sakyamuni to all sentient beings in the universe. It is an education of the wisdom and understanding of life and the universe. In regards to time, it encompasses the past, present, and future. In regards to space, it encompasses everything from our daily lives to the infinite universe. It is not a religion. If one says the teachings of Confucius concerns one lifetime, then the teachings of the Buddha cover infinite lifetimes.
The Buddha taught us that perfect wisdom and virtue are innate to all beings. The sutras, the recorded teachings of the Buddha, tell us that "all sentient beings can attain Buddhahood." and "every being possess the wisdom and virtuous character of the Buddhas in nature. However, due to our discriminating and wandering thoughts and attachments, which are the root cause of all sufferings and disasters, we have temporarily lost our original Buddha nature. Thus, we continue being born into the endless cycle of birth and death."
The more we rid ourselves of the wandering thoughts and attachments, the more we will experience freedom from suffering, and the more wisdom and enlightenment we will uncover. Once we completely free ourselves from discriminating and wandering thought and attachments (our fixations to certain ideas or objects), we will regain our lost Buddhahood, our original perfect enlightened state, and our self-nature Buddha.
Most importantly, the Buddha introduced to us the Western Pure Land of Amida Butsu (or Amitabha Buddha). This Western Pure Land was created by Amitabha as an ideal place of cultivation for all sentient beings. For those who are born in the Pure Land will no longer be subject to reincarnation within the six realms.  This means once we are reborn in the Pure Land, we will be free from the endless cycle of death and birth. Not only that, we will also attain perfect enlightenment and Buddhahood by hearing the teachings of Amitabha in the Western Pure Land. Buddha Sakyamuni has encouraged us numerous times (mentioned in numerous sutras) that we should make a vow to be reborn into the Western Pure Land by practicing the Buddha-name Chanting method. As we are very lucky to learn about the name of Amitabha Buddha and the Pure Land in this lifetime, it is very possible for us to achieve perfect enlightenment and Buddhahood in one lifetime.
For those interested, the goal of Buddhism as an education is well explained on this site of What is Buddhism.
For those interested in the Buddha-name Chanting, here is the simple practice of Amitabha Buddha chanting explained.

The answer to this q should be short and sweet.
The primary and agreed upon definition is as follows:
The belief in and worship of a superhuman controlling power, especially a personal God or gods. "ideas about the relationship between science and religion"
If you agree with the Buddhist concept that reality is a democracy, then no Buddhism is not a religion. There is no superhuman controlling power, nor gods/goddesses. Unless you count yourself, because the the world is in your mind, and you in the world, in other words you're literally creating everything perceived. But this is stretching the definition, so let's stick with No.
Moving onto the the next most utilized meaning, we find religion is a "Particular system of faith and / or worship". Again, Buddhism does not require faith or worshiping anything. So again, No.
Finally there's religion's ancillary definition, which reads "a pursuit or interest to which someone ascribes supreme importance". So obviously Buddhism can easily fall under this descriptor, however since the two most popular definitions don't fit in with Buddhism philosophy, the answer remains, No.

Based on the historical evidence it looks like Buddhism was really the first real complete religion in history contrary to the popular media portrayal or what many of these other answers claim.
There's no scholarly consensus on what defines a religion (https://en.wikipedia.org/wiki/Definition_of_religion).
But looks like almost every post-Buddhist religion in the area was heavily influenced by Buddhism (including possibly Christianity and Islam too)...the Sammasambuddha Gautama originated all types of ideas and concepts influencing everyone around.
Sammasambuddhas are fully enlightened and also the best teachers...they seem to originate religions.
Look at history:

Buddhism originates around the 6th Century BCE
Indo-Greeks (particularly Dharmaguptaka school) spread Buddhism around the world
Concepts found primarily only in early Buddhism start appearing in post-Buddhist Hinduism, Christianity, Islam, and other post-Buddhist religions

Buddhism probably also influenced many other religions unrecorded the influence is unknown but Buddhist relics have been discovered in Hellenistic Egypt.
The majority of world religions don't have detailed debates, explanations, rules, and more than 10,000 suttas they are more like vague practices or beliefs and leave a lot of questions unanswered whereas in Buddhism only a few things are unclear or unanswered.
So it's debatable if other religions are really religions rather than just vague beliefs or practices.
It seems more rational to argue that almost every other world religion is not really a religion...there's no real detail or explanation in most religions just vague beliefs and ideas.
The Vinaya contains hundreds of rules seems like nothing like that is found in any pre-Buddhist religion so in reality Buddhism is the first real religion!
Remember Gautama Buddha was a Sammasambuddha who is fully enlightened and also a supreme teacher, his promise as stated in DN 16:

‘Evil One, I will not become fully extinguished until I have monk
  disciples who are competent, educated, assured, learned, have
  memorized the teachings, and practice in line with the teachings.
Not until they practice properly, living in line with the teaching.
Not until they’ve learned their tradition, and explain, teach, assert,
  establish, disclose, analyze, and make it clear.
Not until they can legitimately and completely refute the doctrines of
  others that come up, and teach with a demonstrable basis.’ (DN 16)

A Sammasambuddha is the supreme teacher (the distinction between a paccekabuddha, arahant, and Sammsambuddha).
This is more like the exact opposite of the popular media portrayal clearly showing Buddhism as the first real religion.
This makes Buddhism distinctly different from other religions which aren't really religions but more like vague beliefs or practices...their teachers never claimed to be supreme teachers or to know much and many never explained anything.
The Sammasambuddha Gautama is the real father of all dhammas...you can clearly see from history almost every post-Buddhist religion being influenced by Buddhism.
It amazes me that such a Super-Being existed in human history...

The word "religion" in Latin means "to bind" usually in the context of taking up a practice or being under a contract.  More generally, it refers to binding as in the act of tying or securing.  It's virtually identical to the Sanskrit word "yoga" which literally means to "yoke" as you would yoke an ox to a plow.
Buddhism is almost unarguably a yoga in the Vedic sense.  It is a practice and a rule of training.  For that reason, I would say it is also faithful to the etymology of the word "religion".

Is Agile Software Development a religion? For some people it may indeed look that way... Do you believe in Agile? Do you subscribe to its system of values, its activities, its daily rituals?
Is Ecology a religion? Do you believe in the global warming?
Is democracy a religion? Do you believe in diversity?
Something may feel like a de-facto religion even without the supernatural stuff. Instead, it seems like every time there's an ethical system of sufficient complexity, some people see it as simply the right thing to do and others see it as a religion.
I suppose it has to do with their level of insight into the principles of that system. The clearer the principles are to someone, the less they see it as a religion, and vice versa.
Which means that to whatever degree Buddhism is lost to confusion and superficial parroting, that's the extent to which it becomes a religion.
Just like Agile Software Development, for some people Buddhism simply makes sense, other people find it puzzling just like the outsiders are puzzled with Agile or with Eco-movement etc., and yet other people happily parrot it at the superficial level, without actually understanding its meaning and purpose. For the first group, Buddhism is not a religion, for the other two, it clearly is.

What people regard as "Buddhism" might be a re-ligion, the again and again falling bond by unskilful identification, good householder.
In regard of what the Sublime Buddha left behind, called Dhamma-Vinaya (not Buddhism), this does actually "Legion" and not re-legion (binding again). It's a legion, one which wasn't one bond before. And to be clear, this legion has also a community, the community of Monks of which is the legion, followed and supported by devoted Lay people who kee this Legion present and alive in the world by material needed means. The Legion, Bound, Sangha and the devoted lay follower forn what is called "Buddha-Parisa" the gathering around the Buddha.
Of what vegetates around outside the Legion, the Parisa, being not this Dhamma-Vinaya, but uses much of that for gains, this is common known as Buddhism, one of the never ending Religions, re-bonds, again ad again.
Books, btw., are not really a means of this Legion, as it requires the bond to teacher on stage, the bond to master, to become part of it. So good to look out for a rightly walking Sangha rather to invest time and effort into gain of books.
[Note that this isn't given for stacks, exchange, other world-binding trades, but for an escape from this wheel]

If following a person 'religiously'(or sincerely) is called religion then Buddhism is a religion. Buddhism is a religion which denies itself. It denies its own existence as absolute just as your existence is not absolute. Buddhism or Dhamma can be 'used' to reach to the shore of Nirvana and then you will have to abandon the religion or dhamma. Most religions follow the guidelines given God. I have generalized the definition of religion by saying following a person's guideline sincerely is called a religion. Under that definition of religion Buddhism stands apart as a religion. BTW , for all practical purposes one can take Buddha as the God, because isn't following such a good person equivalent to following a good God?

Buddhism has now become a religion that is more to do with rites, rituals, icon worship, collection / transference of merits etc., similar to what happens in the sacred places of other religions.
Even whether there is truw interpretation of the true Dhamma contained in the Sutta Pitaka is a question. Buddha Dhamma is more of a clinical evaluation of our existence, a way of life, a philosophy than a religion. So one can say that there is a mundane level and a supra mundane level to it.
It is the same story when it comes to the practice of meditation. There are people who attain ‘anariya jhanas’  or ‘mundane jhanas by focusing the mind on any thought object (vitakka) that come their way. This could be the breath, a kasina object, or any other religious symbol of any religion, and then fixating the mind on this object. This is called ‘vicara’ or sustained application).
For one who contemplates the ‘Tilakkhana’ of anicca, dukkha, anatta at least to some extent, it is possible to attain Ariya jhanas. It is because this contemplation gives rise to ‘niramisa sukha’ or a ‘cooling down’ over time. When one has arrived at such a stage, one can use it in a ‘kammatthana’ to cultivate jhana.  These ‘kammatthana’  are PALI phrases such as “Ethan santhan ethan paneethan, …….” . The thing is one has to know the meaning of these Pali phrases. These phrases cannot be used just as a chanting object without understanding what is meant by it. Even the accepted meaning of the words anicca, dukkha, anatta is questionable.
If one makes a break through and grasp the true meaning behind these words, then the Dhamma would help beings to make a stop to the continuation in Samsara. That is why there is no other philosophy or religion that can be compared with the Dhamma taught by the Gautama Buddha.

Buddhism is not a religion. And it has not become a religion. But people have label it as a religion due to the misunderstanding and lack of wisdom within them to understand the core of buddhism.
If I ask you Is Newton's law of universal gravitation, a religion? The answer would be No. Same goes with Buddhism. And in buddhism the complex law of the nature is explained. And also Buddha has found the problem of this world and also the way to exit from it. So Buddhism is not a religion but for the people who is lack of wisdom it is.

The essential teaching of Buddhism is to make us experience who we really are. Experience is Primary. The Buddha having experienced for himself who he really was, gave us the Method, to enable us to follow the Path he took.
The Vision behind the Method is called Nirvana, or Nibbana or Enlightenment. This is what we need to experience. In order to reach this Vision, the Buddha gave us many Missions to accomplish. These Missions are technically referred to as the 37 x Aids to Enlightenment. There are countless books on the internet and videos on youtube to show you the 'theory and practicals' that go to make the Method. It is the Method that makes Buddhism unique. If not for the Method, Buddhism would perhaps be like most other religions. What is unique about the Method is that at its deepest level, it is always one step ahead of the world of Science or more specifically of Quantum Physics. Thus Buddhism is also a Science because, with the help of the Higher Doctrine called Abhidhamma, it can spell out scientifically how each benchmark on the way to Nibbana could be reached. For a non-Seeker Buddhism has become a religion. But for a genuine Seeker it will remain a philosophy that shows you THE WAY.

Are you listening and practicing it or is it applied as state of thinking?
The physical aspects of it as a religion are very real but buddhism is uniquely awake to the problem with organized religion. people come to believe then their fate is a fact and shouldn't be questioned. Logic says if they are doing right and that indicates others do wrong. You also keep people organized under a United front as an organization. Well if it's organized it must have guidelines well those guidelines provide powers and powers tend to corrupt. Also those rules or documents are eventually going to format as valuable information. But that information stands in front of the point.
if you find Buddha you should kill him or see the god kill him. It gets in the way. There's no way to have the cake at eat it too. So no, it a religion but not a religion. Ask a Buddha. If you're looking at Buddha as a god that is not his aspect. There are others for that and that's part of the point. He knows only what you don't that's the only difference. So if you know what he does who does that make you? How do you learn what Buddha knows?

There is a karmic flow here that we should all pay attention to. Allow me to put some words to it, even though the words are imperfect...

Philosophy: Someone comes along who attains a deep understanding of the world, and tries to convey it to others. This may start as an insight or a revelation, but ultimately what this person tries to convey is a philosophy of living.
Faith: This philosophy attracts followers, who don't (at least initially) share the originator's deep understanding, but believe in it wholeheartedly. These followers develop the three jewels: a reverence for the teacher (who slowly passes into memory), a community of believers, and a set of teachings and practices meant to bring the believers to understanding. That is the heart of a faith.
Religion: This faith develops ever more followers, ever more remote from the original teacher. They create rituals, songs, temples, works of art; they make orders and hierarchies and modes of authority; they embellish the teachings and practices, solidifying them as forms without living their substance. That is the essence of religion: a formalized and stylized exposition of the faith.
Culture: The religion dissipates to such an extent that its teachings are mere dogma and its structures and rituals are superficial badges. We say we are 'this' religion or 'that' religion because that's what our parents and friends are, and we do battle with others because they say they are something else (because of their parents and friends). To paraphrase the daodejing, this state is the empty husk left behind as a religion dries up and dies.

Of course, anyone can work their way back up this chain, swimming against the karmic stream in an effort to recapture the original philosophical understanding. That is the meaning of dharma. While religions may die and faiths may weaken and fade, understanding is eternal, and it is always possible to reach for it. But regardless, we will always find people at every stage, engaging the understanding in the best way they now how (however limited that might be).

For many people, Buddhism is just a part of the culture: a voice in that background of noise that fills their minds.
For many others, Buddhism is a religion: they pray to the Buddha, light incense, ring bells; they chant and sing and prostrate themselves to the altar.
For a few others, Buddhism is a faith: they diligently work the practices, devote themselves to the teachings, and strive for the understanding.
For a very few, Buddhism is a philosophy: it is something they understand and live; not something they know and do.

The question is, which of these do we want to call 'Buddhism'? Are all of them Buddhism, or none of them? How we answer that question says more about us than about Buddhism, I suppose, so I suggest we take it as a koan.


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If no sentient being exists, for whom is there compassion? 'A Guide to the Bodhisattva Way of Life' by Santideva
Quoted below is from 'A Guide to the Bodhisattva Way of Life' by Santideva, Chapter IX: The Perfection of Wisdom. I'm struggling to follow the line of thought, can someone please decipher what it means.
This is what I deduce reading it and It really is incomprehensible to my feeble mind.

Sentient beings do not exist
For one to be compassionate he has to be deluded to believe that sentient beings exist.
Compassion itself is a delusion
One should remain deluded to alleviate the nonexisting suffering of nonexisting sentient beings.

How can all this be true?
Please note I'm writing bluntly because I want to understand what it means not because of lack of respect for Santideva work, far from it his book is always in my heart... it just that I can't get through chapter 9 :/

[Qualm:] If no sentient being exists, for whom is there compassion?  [Madhyamika:] For one who is imagined through delusion,
  which is accepted for the sake of the task.
[Qualm:] If there is no sentient being, whose is the task?  [Madhyamika:] True. The effort, too, is due to delusion.
  Nevertheless, in order to alleviate suffering, delusion with regard
  to  one's task is not averted

First, you have to keep in mind that Shantideva's work is versified. This implies that it is not always technically accurate, because words are missing for the sake of poetry. For instance, we will read "sentient beings do not exist" as "sentient beings do not exist inherently" implying "but they do exist conventionally." What does not exist is a mode of existence.
Second, Shantideva was a Prasangika. This is his view of emptiness that neither persons nor phenomena exist inherently. They do exist conventionally. Prasangika also posit that conventional valid cognizers in the continuum of ordinary beings are valid with regard to the entity of the thing, but mistaken with regard to the mode of existence of said things. This all helps you understand that we do not negate conventions.
Third, Gyaltsab Je wrote a Prasangika commentary to Shantideva. He explains verse 9.75 as follows:

Gyaltsab Je: Realist: If there is absolutely no inherently existing
  person, then, as there is no focal object for compassion, for whom
  should one practice meditation on compassion? Madhyamaka: If there is
  no inherently existing person, then it follows there is no such fault
  that the focal object of compassion is non-existent, because that
  nominally existing sentient being, labelled by mental darkness, which
  is accepted for the purpose of achieving the result of liberation, is
  valid to be the focal object of compassion.

While part of his commentary on verse 9.76 says:

The opponent says that if sentient beings do not exist inherently they
  do not exist at all. The question is that if sentient beings do not
  exist, who would experience the result of meditation on compassion
  that is buddhahood? It is clear that the object of observation as well
  as the result of the meditation on compassion do not exist truly, but
  the problem as posited by the opponent does not exist for us, in that
  sentient beings still exist conventionally, and therefore
  conventionally it makes sense to meditate on compassion.

Now, to answer your questions more directly:
1) Sentient beings do not exist
They do not exist inherently (or truly), they do exist conventionally. A valid eye consciousness apprehending a person is valid with regard to the entity of the thing. Compassion towards a person is valid with regard to the entity of the thing as well. Compassion towards a unicorn, however, is not.
2)For one to be compassionate he has to be deluded to believe that sentient beings exist.
No. For one to be compassionate, he has to have some sort of insight into the four noble truths. Also, he who believes that sentient beings are utterly non-existent is deluded. So is he who believes they exist inherently (which is the whole topic here).
3)Compassion itself is a delusion
It is not, because a delusion is never valid with regard to the entity of the thing. For instance, anger does not engage its object correctly. The object [of engagement] of anger is as non-existent as a unicorn. In addition, delusions take away the peace of the mind (it's their definition) and superimpose.
4)One should remain deluded to alleviate the nonexisting suffering of nonexisting sentient beings.
This is not the case, since the conventionally existent buddhas do alleviate the conventionally existing suffering of conventionally existent sentient beings.

Non-versified books you can read on the topic are:
1. Commentary on Shantiva

Gyaltsab Dharma Rinchen, The Entrance for the Children of the Conquerors, A Commentary on Shantideva’s Introduction to the Actions of Bodhisattvas

2. Madhyamika

Elizabeth Napper, Dependent‑Arising and Emptiness

3. Special Insight

Je Tsongkhapa, Lam Rim Chen Mo, Volume 3, Part 2
Je Tsongkhapa, Middle Length Lam Rim, Chapter Five
Guy Newland, Introduction to Emptiness
Guy Newland, The two truths
Jeffrey Hopkins, Tsongkhapa's Final Exposition of Wisdom
Khedrup Je - A Dose of Emptiness

Thanks @ Tenzin. If you don't mind  can you give response for each four statements in both truth ( conventional and ultimate). I ask this because i want to see these completely distinct.

Also if you don't mind could you please direct me to a book or any writing in English which deals with this analytically, i mean not 'versified' as you noted. Thanks a mil.

@user12952 I added titles of books. However, I am not sure I understand what you mean with "giving response for each four statements in both truths". Especially, which four statements are you referring to?

Thanks for the list of book @Tenzi..'m truly grateful!..........................The four statements that i refer to are the four statements that you gave direct response to i.e.  ...1)Sentient beings do not exist....2)For one to be compassionate he has to be deluded... etc... I think in the ultimate reality all four seem to be true as i stated them originally.

@user12952 You are most welcome. I'm sorry but I don't understand what you mean with "giving response for 'sentient beings do not exist' in both truths." That sentient beings do not exist is not true. However, you can say sentient beings do not exist inherently. Or sentient beings do not appear in the perspective of a non-buddha directly realizing emptiness.

Let me quote Dogen's Genjō Kōan:

When things are seen in context of Buddha-Dharma, there is "delusion vs enlightenment", "practice and study", "birth", "death", "Buddhas" and "sentient beings". When things are seen in context of Emptiness, there is no longer such thing as "delusion" and no "enlightenment", no Buddhas, no sentient beings, no birth, an no death.
The path to buddhahood starts with a feeling that
  there is "too much" of one thing and "not enough" of another, and in that context there are "birth" and "death", "delusion vs enlightenment", "ordinary beings" and "Buddhas". But in reality this feeling only comes from attachment to a certain perspective, just like when we get nostalgic over the blossoms’ withering but hate when the weeds are flowering.
To undertake the project of Enlightening the entire universe through one’s training while carrying the burden of self is a delusion. To have the entire Universe enlighten oneself through training is awakening. To have awaken to one’s delusion is to be enlightened -- and to be deluded about enlightenment is to be an ordinary being.

To take on your individual statements:
1) Sentient beings do not exist
Incorrect. From the perspective of someone who sees, things are beyond descriptions such as "sentient beings exist" or "sentient beings do not exist". The idea of "sentient beings" is but one way to describe reality.
2) For one to be compassionate he has to be deluded to believe that sentient beings exist.
Incorrect, "he" is not deluded, he's just able to understand the delusion of others. Empathy or compassion is an ability to imagine what the world looks like from another perspective. Because those who see the truth have such ability (as they attained the truth by completely and utterly letting go of their fixed perspective), they can see reality from a perspective of a description that uses the concept of "sentient beings" and all that goes with it. And when you see things from this perspective, you see suffering, birth, death etc. -- all that stuff exists from the same perspective.
3) Compassion itself is a delusion
Incorrect, compassion or empathy itself is a real skill. In cognitive science, being able to understand what the world looks like from another observer's standpoint is a key criteria of sentience.
4) One should remain deluded to alleviate the nonexisting suffering of nonexisting sentient beings.
Incorrect, to be able to understand different people and to ferry them across, one needs to be able to see reality beyond limitations of a single perspective, and to freely move between perspectives.

For others, what is just a mere delusion, is not a mere delusion, but reality.
For you, an enlightened being, there is no suffering, no sorrow, no pain, no happiness, no beings, no life, no death, no nothing, etc.
For others, not enlightened beings, there is suffering, sorrow, pain, happiness, beings, life, death, nothing, etc.
Because there actually is suffering, sorrow, pain, happiness, beings, life, death, nothing, etc. the Bodhisattva has compassion and it is the right thing to do because there actually IS suffering, sorrow, pain, happiness, etc.
UPDATE:
So you think everything is empty, thus there is nobody for whom to be compassionate. And now you're wondering if there is no object for compassion, then why compassion? For whom compassion, if there is nobody to be compassionate for?
The answer is in verse 75: "For one who is imagined through delusion". Thus, compassion is for nobody, but since this nobody actually IS somebody, that's why there is compassion for this somebody.
Even if a Bodhisattva knew that this somebody is actually nobody, he would still continue to be compassionate for this nobody because this nobody is deluded to be somebody. For nobody thinking he is somebody, there is suffering, sorrow, pain, happiness, beings, life, death, nothing, etc. and because for somebody there actually IS all this, this somebody is subjected to suffering. Even though there is nobody who suffers, there actually IS somebody due to him being deluded there is somebody and for him (the deluded one) there actually IS somebody who is suffering.
"For one who is imagined through delusion, which is accepted for the sake of the task." does not necessarily mean "For one to be compassionate he has to be deluded to believe that sentient beings exist". It can also mean "For one to be compassionate, other beings have to be deluded to believe that sentient beings exist".
In verses prior to verse 75 it says that the "I" cannot be found. Whenever the "I" is found, that is not the "I". Examples of this are here:

"73. The past or future mind is not "I," since it does not exist. If
  the present mind were "I," then when it had vanished, the "I" would
  not exist any more."
"74. Just as the trunk of a plantain tree is nothing when cut into
  pieces, in the same way, the "I" is non-existent when sought
  analytically."

To an uninstructed mind, it would logically follow that compassion is not needed, that's why this question arises:

[Qualm:] If no sentient being exists, for whom is there compassion?

And this is the answer:

[Madhyamika:] For one who is imagined through delusion, which is
  accepted for the sake of the task.

Given that the author in prior verses says that there actually is no "I" for whom to be compassionate, the only possible interpretation of the above answer can be this:

[Madhyamika:] For one who is imagined through delusion by the
  Bodhisattva or by the being, which is accepted as real by the
  Bodhisattva for the sake of the task.

If compassion would not be needed, there wouldn't be a long debate "why compassion is needed" and there wouldn't be the answer that compassion is needed for the one who is imagined through delusion. The "one who is imagined through delusion" does not cease to exist when the Bodhisattva eradicates his delusion nor when the being for which the Bodhisattva is compassionate eradicates his delusion. "one who is imagined through delusion" ceases when both the Bodhisattva and the being eradicate their delusions. When both eradicate their delusions, "one who is imagined through delusion" ceases to exist, there is no more suffering, no sorrow, no pain, no happiness, no beings, no life, no death, no nothing, etc., thus no more compassion is needed between the two because suffering actually ceases for both of them, comes to an end. Thus, until both eradicate their suffering, compassion is needed. As long as there will be deluded beings, compassion will be needed.
In the same way as verse 75, verse 76 can be interpreted.
The verse that follow then has sense:

However, grasping onto the "I," which is a cause of suffering, increases because of the delusion with regard to the Self. If this is
  the unavoidable result of that, meditation on identitylessness is the
  best.

I would interpret it like this:

However, grasping of the Bodhisattva onto the "I," which is a cause of suffering, increases because of the delusion with regard to the Self. If this is
  the unavoidable result of that, meditation on identitylessness is the
  best.

UPDATE 2:
You are indulging in the view "Sentient beings do not exist".
You think that sentient beings are just a dream. Thinking so, you think that once you wake up, sentient beings would vanish, because they haven't ever existed in the first place, isn't it? For you, sentient beings are non existent, isn't it? You think sentient beings are just characters in your dream, isn't it? You think that I and other sentient beings don't exist. That's what you think and that's the reason you're not satisfied with the answers.
You think that my dream is part of your dream. You think that my dream does not exist and that it's just part of your dream. That's not true. Your dream is your dream and my dream is my dream. They are two separate dreams. When you wake up from your dream, I'll still be in my dream. When you wake up from your dream, this world and the sentient beings in it would not cease to exist - they would still be in their dreams. But you, because you think that they are all part of your dream, think that they wouldn't exist anymore, which is incorrect.
Just think about all sentient beings who woke up from their dreams. If we were just a dream, after a sentient being woke up, then you and me would vanish and would not be here. But you and me are still here, even though numerous sentient beings woke up. How could that be?? They all woke up from their dreams, but we are still here? If we, sentient beings, were just a dream, we would vanish the moment a sentient being woke up. But that's not the case. We're still here, even though others woke up. Why we're still here?
Is it maybe because every sentient being is in his own dream? Yes, that is the answer.
Wrong view is: when I wake up from my dream, other sentient beings will stop dreaming because they haven't ever existed in the first place because they were just characters of my own dream.
Right view is: when I wake up from my dream, other sentient beings will continue to be in their dreams.
It is wrong view to say "Sentient beings do not exist". Right view is "Sentient beings neither do not exist nor exist" and even this view is wrong if not understood properly. Correct is to let go of all views:

"Does Master Gotama have any position at all?"
"A 'position,' Vaccha,
  is something that a Tathagata has done away with. What a Tathagata
  sees is this: 'Such is form, such its origination, such its
  disappearance; such is feeling, such its origination, such its
  disappearance; such is perception...such are fabrications...such is
  consciousness, such its origination, such its disappearance.' Because
  of this, I say, a Tathagata — with the ending, fading away, cessation,
  renunciation, & relinquishment of all construings, all excogitations,
  all I-making & mine-making & obsessions with conceit — is, through
  lack of clinging/sustenance, released."
Source: http://www.accesstoinsight.org/tipitaka/mn/mn.072.than.html

You are caught in a view "Sentient beings do not exist" which is one extreme:

"By & large, Kaccayana, this world is supported by (takes as its
  object) a polarity, that of existence & non-existence. But when one
  sees the origination of the world as it actually is with right
  discernment, 'non-existence' with reference to the world does not
  occur to one. When one sees the cessation of the world as it actually
  is with right discernment, 'existence' with reference to the world
  does not occur to one."
"'Everything exists': That is one extreme. 'Everything doesn't exist':
  That is a second extreme. Avoiding these two extremes, the Tathagata
  teaches the Dhamma via the middle
Source: http://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.015.than.html

You are caught in non-existence. You should let go of it and come out in the middle. It's because of the extreme "Sentient beings do not exist" that you can't see a reason for compassion.
The whole point of enlightenment is to avoid extremes and come in the middle.
Once you come in the middle, you will know that your dream is your dream and my dream is my dream, so even if you wake up from your dream, there will still be my dream. That's why compassion remains and that's the reason why compassion can continue to go on, even after awakening/enlightenment.

Thanks @beginner.. But the question has something more than you described. Imagine you and your companion walking in a desert, your friend seeing a mirage think that there is water ahead and become joyful, but you, knowing what a mirage is, compassionately try to convince your friend not to be deluded hoping to alleviate his suffering when the mirage turns empty. This analogy fits well with what you described. However, the question goes beyond this .. You as an enlightened being also knows that your friend is also a mirage the same as the none existing water. So, for whom is there compassion?

Compassion is for one who is imagined through delusion. Even though you're enlightened and you know your friend is a mirage, your friend is not enlightened and he thinks he is not a mirage. He can't yet comprehend what you know and maybe he would need many more years to comprehend it. That's why you're compassionate. You're compassionate towards nobody, but because your friend is not enlightened, you are really compassionate towards somebody (not nobody). And you accept it for the sake of the task. I updated my answer for a more detailed explanation.

tanks for your effort...Let me try another simile for your verification...sorry i like similes... What you described seems to me like someone [Bodhisattva] in a dream and when he realize that he is in a dream with his eyes closed continue the dream story feeling compassionate to the characters in the dream. In the dream the Bodhisattva also has a character an 'I'  and if he meditate on identitylessness.. what happen then does he wakes up? .... This is profoundly complex, but i ask because i think within it the answer as to how one can embody both dispassion and metta is contained.

Until the Bodhisattva is not enlightened, your simile is correct. But once the Bodhisattva becomes enlightened, he opens his eyes and he is not in a dream anymore. Then he sees beings who are still dreaming. He knows how much they suffer because of their dream, so he does what he can to alleviate their suffering. He is out of his dream, but others are still in their own dreams. He knows that. He can't deny it.

That which for an enlightened being is a dream, is reality to the unenlightened being. You can't deny that, you can't just erase it. It is there. Because it actually is there, an enlightened being helps others by being compassionate.

Sorry for the multiple comments, but i think you are still leaping over the central question. Following the same analogy, the one awakened has to go back and sleep or dream (in other-word be deluded) to be compassionate; that is because he can only see suffering beings in his dream.

No problem for multiple comments. If you go into a dream and know that you're dreaming and you ask yourself "Is this real or it's just a dream?", what would you answer? You would answer that it's not real, that it's just a dream. So even though you're dreaming, you're not deluded. You are totally aware of the dream. In this way you don't have to be deluded in order to be compassionate. But now I guess you're still not satisfied with this explanation, because you're thinking "If everything is just a dream, then why don't just forget about compassion and wake up from the dream?", isn't it?

Exactly, that is the question! Why dream?

I see. I updated the answer. Maybe it will help clarify things.

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Buddhism and Evolution
I heard an atheist ask this question from a christian and found myself lost in this question as well.
Plainly and simply the question is this,

How does your religion fit into earth's history?

His point was that although many religions talk about a very old human race, we are a new species. even if we deny all the archaeological evidence, we still can't answer how such a human civilization escaped the few annihilation earth faced, like the long ice age and the meteor that killed the dinosaurs etc.
Do we as Buddhists have an answer, considering we believe in an even older human race's existence?

When the Atheist asked his Christian pal about the evolution of this race, there is only some variations of one answer that our education system, the media and so-called information technology promotes. They are the main instruments used by the Western Christian countries in the present day. There is no freedom of knowledge or of media as there is no second opinion given at any time. It is what this ideology decides that is given to the public. The so called alternative view is only another version of the view of the western Christian mindset and people have no choice in this matter. Even today creationism is allowed to be taught in schools and Darwinian evolution and creationism are nothing but twin systems that try to give an answer to the question how the world (universe) was created and then evolved.
What Buddha said on this is found in the Agganna sutta. Agganna Sutta is the 27th Sutta of Digha Nikaya collections. The sutta describes a discourse imparted from the Buddha to two Brahmins, Bharadvaja and Vasettha, who left their family and caste to become monks. These were two brahmins who were insulted and maligned by their own caste for their intentions. But what is important for us here is that the qualities of the Dharma (Law, truth) is the same as the qualities of the Buddha and forms his "truth body" or "Dhamma Kaya”. A reference from the Agganna Sutta says to his disciple Vasettha:
"Tathagatassa h'etam Vasettha adivacanam Dhamma-kayo iti pi ...":
O Vasettha! The Word of Dhammakaya is indeed the name of the Tathagata.
Dhamma in Buddhism has two primary meanings: the teachings of the Buddha which lead to enlightenment, and the constituent factors of the experienced world. A sankata is an entity arising due to a sankhara; a sankhara is also a sankata, because just like any other sankata, any sankhara arises and falls; thus sankhara is sometimes used to include both. However, a sankata is normally something that arises due to sankhara  (a living being, house, nest, a thought, hopes and dreams, etc) and eventually is destroyed. Nothing in this world lasts forever.
At the deepest level, anything in this world arises due to the mind. That is what was meant by the Buddha when he said, “manopubbangama dhamma……” or “mind precedes everything else…”. It is this that gets described in detail in the Agganna sutta.
In that sutta, the Buddha explains how conglomerates of “planetary systems” blow up and are re-formed in time scales of “mahā kappas“. He has given a simile to get an idea of the length of a mahā kappa and it is approximately several billion years. And this destruction of a “star system” seems to be what scientists have observed as a supernova. Supernovae are of common occurrence; about three of them can be expected to happen every century in our Milky Way galaxy.
A suddhāshtaka is a “packet of energy” and is the basic unit that all matter is made out of. It is much smaller than in energy compared to a light photon that we see. A humongous number of suddhāshtaka would have the energy of a light photon. A suddhāshtaka, being a sankata, is created by the mind. This is why the Buddha said, “manō pubbangamā dhammā…”, i.e., “everything has mind as the precursor…”.
It is a valid question to ask and observe that in the few annihilation that earth faced, like the long ice age and the meteor that killed the dinosaurs etc., the “what if so? questiion.When the human and animal realms are destroyed, all those beings would be reborn in the first rūpa realms. When that is gradually destroyed, they will be reborn in the next higher realm and so on, until they are all in the Abhassara realm.
Buddha’s explanation of how all living beings in the lower realms get into the Abhassara Brahma realm when our world system (Cakkavata) is destroyed is not properly explained in any text found online. When the Sun starts heating up, fine sense objects start being destroyed, and with time less and less sensual objects will be there to trigger kāma rāga. All humans and animal will move to higher realms (over an antakkappa which lasts billions of years).
Even though all dense material realms are all destroyed at the end of a world cycle, all rūpa and arūpa realms at or above the Abhassara realm remain intact. When the Solar system is “re-formed” after billions of years, they all gradually come down to lower realms. . In the future, it will become clear to us that anything in this world has origins that can be traced back to the mind. That is the story in the Agganna sutta.

I doubt some of the statements in the first paragraph: I think that Western countries tend to be more atheist now (in recent generations) than Christian; and I doubt whether creationism is taught in schools, in America or in Ontario, except in "religious studies" classes.

Thank you my friend, I completely agree. But i have some questions about this part, Theravada Buddhism speaks of this being a special Kalpa. According to the canon, we have had few Buddhas in this Kalpa and the next Buddha is the last one for this Kalpa. But the thing is that we have not existed long enough on this planet that long to receive the teaching of lord Buddhas....

Note that this end of days scenario you mention come at the end of a Kalpa and we have yet to reach the end of this one. So all the Buddhas mentioned as the ones of this kalpa came and went while no disasters of that magnitude happened. This is the gap i am curious about.

The Baroque Era broke the old rules of the traditional Renaissance. Similarly Charles Darwin's Theory of Evolution by Natural Selection took over the Adam & Eve in Paradise line of thinking, but it is still Christian. What matters to us is that you and I are fortunate enough to live in a very special time when the True Dhamma of Buddha has resurfaced, and a sea change is taking place right now. So be open to it. The 2012 phenomenon was this. It was the end of one cycle and the beginning of another. It is happening in Sri Lanka right now & may take a few years for others to get to know of it.

Well that is my country too, i have no intention to talk of darwin. What i  mean is that we speak of ancient kingdoms in india in the canon but what we can see if we go to a indian natural history museum is that india was full of dinosaurs and other contemporary creatures instead of humans in the described timeline.

I am agnostic (which can mean, literally, "without knowing") of an even older race's existence.
Some (many) people understand the Agañña Sutta to be a "parody", of contemporary Brahmanical texts -- see e.g. this answer, or this answer.
There are suttas which mention "no discernible beginning"; and which list "unanswered questions".
See also "akalika" -- i.e. the dhamma being timeless, immediate.

The various historical theories seem to me plausible (or well-argued and widely-agreed by experts given the archaeological evidence ... but not, so far as I know, very relevant to Buddhism), e.g.:

The Buddha lived about 2,500 years ago
The most recent glacial period ended about 10,000 years ago
Anatomically modern humans have existed for about 100,000 years (but modern behaviour including language and "stone age" tools for only about 50,000 years), contemporary with the most recent ice age

What about the stories mentioned in the scripts that talk about kingdoms and civilizations with humans with a life expectancy of about 60000/200000 years and etc. those civilizations couldn't have existed according to modern belief.
You're asking about this kind of thing: First antarakalpa (Buddhist cosmology).
I see that the suttas this comes from (e.g. DN 17 and DN 26 and DN 14) aren't translated on Access to Insight.
Here is a comment on how the translator/editor selected which suttas to include on Access to Insight:

The emphasis here is on practice. For the most part I selected books, articles, and sutta translations that I personally found helpful to develop a better understanding of the Buddha's teachings, rather than texts that tend to fuel intellectual debates on abstract philosophical concepts.

Your question asked "Do we as Buddhists have an answer, considering we believe in an even older human race's existence?" --

I think it's possible for Buddhists to not have that belief (being "agnostic" means you also don't have to deny or contradict the belief)
If I answer your question about "we", I don't or didn't mean to answer that everyone believes or doesn't believe as explained in this answer. I don't doubt there are some Buddhists who "believe", who may try to reconcile it with (explain it in the language of) modern science, perhaps using words like "other solar systems" or "other universes" etc.

My initial (school) training is more-or-less as a Physicist. My opinion is that every time I see people try to relate Buddhism to Physics, they're wrong (i.e. confused) -- but people do try, you can see it sometimes on this site, trying to relate Buddhism to Einstein's relativity, or to quantum mechanics.
Anyway I think that in general Buddhism describes human perception and psychology (how we feel about the world, how we think, subjective), and sociology (ethics in society), and philosophy (what "good" is, and which are the better "views") ... none of which is in the domain of Physics.
So, I assume that the Agañña Sutta (if it's worth considering at all) is saying something about Buddhism, about human experience (psychological being), and not about Physics (form, astronomy, geology, species etc.). For example maybe the sutta is about the experiences of a single human, and the "long lifetime" at the beginning might be some memory of how the days seemed long when you were young, or something like that.
Anyway, have you read the Agañña Sutta? Does it read to you like a story that you're meant to take literally?
Being from a non-Buddhist background I'm accustomed to reading stories, which aren't meant to be literally true, but which are meant to convey a lesson; including:

Christian parables
Muslim pedagogic anecdotes
Children's tales and fables from all over the world, every times and place, e.g. here and here, and these from Ancient Greece whose author lived maybe just a generation before the Buddha.
I'm inclined to put the Jataka tales in the same category, and some of the (prose) tales in the commentaries (e.g. this one) which illustrate the Dhammapada.

Have you read the Rigveda and the Upanishads? It seems to me that the Agañña Sutta is of that style:

Told to Brahmins
Using a literary style (a "creation myth") which the Brahmins would be familiar with, and which were even part of their trade (wasn't it the Brahmins' job, i.e. their social responsibility and privilege, to study and teach this kind of myth)
Adapted to convey (or teach) Buddhist values, including some lesson about desire and food and impermanence, and other concerns like that which we know of from other less fanciful, more straightforward suttas.

Takes the story of "the fox and the crow and the cheese". It's an OK story, about flattery, and getting distracted, and loss, and not sharing; it would be missing the point, IMO, to assume that there must have been a (physical) world in which animals could talk to each other like humans do (it's a fictional world).
Anyway, that's my opinion, in more detail.
I'd like to say this, if I may, in answer to this question, but without wanting to disrespect other Buddhist suttas, about the four noble truths and three jewels and so on.

Thank you for the answer, I think i should give some elaborations here. It is not about Lord Buddha's life time. What about the stories mentioned in the scripts that talk about kingdoms and civilizations with humans with a life expectancy of about 60000/200000 years and etc. those civilizations couldn't have existed according to modern belief.

@Theravada I edited my answer, above, to try to address your comment in more detail.

Thanks friend, i must study more on this. We Buddhists seems to have a loop back when it comes to talking about this kind of things. I must confess that i am at a point of doubt about which part of canon is real and what part is fiction/learning material. As a theravada Buddhist, i never saw any monk or layman take buddhism the same way Christians take their canon, we have been always taught to take the canon as is without any personal interpretations. ....

After comparing the evolution of life on earth to timeline mentioned in the canon about past lives of Lord Buddha & others, there seems to be some differences. I should look into this more. Thanks again!

There are Christians who are taught to believe that, by carefully counting the number of generations told in the Old Testament since Adam and Eve, therefore the earth was created only about 6000 years ago! That theory is popular, in the States; it's a subset of Christian fundamentalism. But the (larger) Catholic Church (and Orthodox Church) does not require such belief.

Yes I (personally) assume the Buddhavamsa may be classified as anhistorical.

Perhaps you won't find monks who deny belief. Occasionally someone (and bear in mind that I tend to only read English fluently) will say something like this (talking about the Jataka tales): "Probably, though, it is more common for Theravada Buddhists to accept the stories far more at face value than they really should, again given their content.". Or (someone else) in this answer who emphasises that "the Buddha’s teaching is FOR THIS VERY LIFE", and akāliko and ehipassiko.

But my friend, Akaliko ehipassiko means, Does not belong to a time and therefore it's timeless + can be realized within a lifetime. It carries no connotations about Dharma being a thing for this life itself and not for many.

@Theravada I'm not trying to argue that topic (about past lives), only trying to answer your question here. I think that people (monks too) may just not pay much attention to some suttas (like the Agañña Sutta): if it deals with an unknown or unknowable topic, a topic which you must be agnostic about, then it's not interesting, not related to the goal, not useful to you (it was intended for Brahmins 2500 years ago). When I do pay attention to it, the way it makes most sense to me is as a story, an allegory. If I were asked how Buddhism fits into history, I might want to say that it's timeless.

I didn't mean that you argued mate, to be honest i have been faced with a couple of questions that made me question a lot of my beliefs. this inquiry is about that.

During ice age we wore animal skin and cuddled near big fires.
Before the meteor fell we gathered food and hid in caves.
Why?
Because of karma.

A longer answer is expected my friend, this is a deep question and can't be generalized this way.

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What else do people who have realized Nirvāṇa do besides teach?

There are numerous references in Buddhist literature to men and women living ordinary, normal family lives who successfully practised what the Buddha taught, and realized Nirvāṇa.

--What the Buddha Taught.
What else do people who have realized Nirvāṇa do besides become teachers? Can you cite examples?

They lay back and chill.

Some get cooking classes.

I wanted to say something funny, but it would be completely inappropriate and out of character ;P

They do what is right.
If they have family to support, they support the family. If they need money to survive, they work. If they are hungry, they eat. If they need a car, they drive a car. etc.

Apparently lay arahants have to become monks immediately after enlightenment according to Milindapanha. If that's the case, they can't support their families or work. See this question and this forum discussion.

@beginner I won't need examples. Your answer make a lot of sense to me.

those who realized Nirvana can do any good thing but they don't produce any result example , suppose an Arahant gives alms , he does not get 'kusal' or merits he has only actions which don't give any positive or negative results.


text:
Is it complete shut down of perception and detachment of physical world?
As we know people who stay in coma or unconsciousness "experience" timeless,space-less, absolute emptiness and total detachment from physical world. Even though I used the word "experience" will not suitable to describe the situation in coma or unconsciousness state. It is a condition with no happiness or sorrow, no pain,no darkness or light,no noise or sound etc....and finally we can say "unconditional state of mind." and closer to description of "Nirvana"

what happen when person die during the coma or unconsciousness state?
Is this similar to Nirvana? (as total detachment of world.)

It is said that those in a come are sound asleep are in a Nirvana-like state but remain in a state of ignorance and non-awareness. Only the enlightened would enter this state awake and unconfused. (I personally can make no comment). You might like to read up on 'turyena'. . .

It is a condition with no happiness or sorrow, no pain,no darkness or light,no noise or sound etc....and finally we can say "unconditional state of mind." and closer to description of "Nirvana"

Actually that's far from Nirvana. If that was the case any sleeping newborn baby would've been in Nirvana without the need for any Dhamma cultivation. A person in a coma might seem to be at peace and without happiness or sorrow, but hidden in those deep layers of his consciousness are still the seeds of defilements, of greed, hatred, and ignorance. As long as these "fuels" are still there and have not been eradicated, the Samsara cycle still goes on for him. In constrast, a person who has attained Nibbana has perfect awareness, but due to the total elimination of all the "fuels", s/he's able to be 100% at peace while being 100% conscious.

No.  If you are unconscious or in a coma then you are not laying there in a blissful state.  Chances are your bodily functions are ticking over and there will be some brain activity.  Just not enough to say or do anything.  You can get a "lock in" syndrome where you can think but just not move your body.  To the outsider you appear unconscious but you are fully awake inside.
There is a HUGE difference between actively "doing right thing" and "not doing something bad" because you are unconscious.  If you were made unconscious while holding up a bank, then you will probably still have bad thoughts.
No, it is not nirvana.  Nirvana is you coming to terms with the world, and your place in it.  It is not imagining yourself floating on a sea of lotus petals.  If you die in a coma, you don't get to say goodbye to anyone.

This is what happens. When a person dies during coma or unconsciousness state, that person comes out of coma, becomes conscious.
This is not similar to Nirvana.
Nirvana is understanding the cessation of thoughts.
Coma and unconsciousness are continuation of thoughts. Coma and unconsciousness do not lead to the understanding of the cessation of thoughts.
The word "during" during coma or unconsciousness does not apply. It applies only to you who is consciouss. To the one who is in a coma or unconsciouss state, it does not apply. Thus, there is no "during" for the person in coma. There is only "now" and "now" for the person in coma. "Now" before coma and "now" after coma. "During" is only for you who is not in coma. What is between "now" and "now" for the one in the coma? Is there something? Or is there nothing? I guess you must find out.

As we know people who stay in coma or unconsciousness "experience" timeless,space-less, absolute emptiness and total detachment from physical world. Even though I used the word "experience" will not suitable to describe the situation in coma or unconsciousness state. It is a condition with no happiness or sorrow, no pain,no darkness or light,no noise or sound etc....and finally we can say "unconditional state of mind." and closer to description of "Nirvana"

In theravāda, this question's base-knowledge is ucchedadiṭṭhi, diṭṭhadhammanibbāna [nihilism&hold the doctrine of happiness in this life], rūpa-attato-sakkāyadiṭṭhi [form (the body) to be the self].

what happen when person die during the coma or unconsciousness state?

In abhidhamma, person still has mind's arising until person's citta-ja-rūpa, such as breathe, still going on. But because of karmma (kamma), temperature (utu), and nutrient (āhāra) are not good enough to support mind to done mind's job, such as making-nerve-impulse (citta-ja-rūpa), etc. So, the tool of the scientist can't catch mind's arising of this person.
That's the reason why some vegetative state can awake again, after long sleeping.

Is this similar to Nirvana? (as total detachment of world.)

Definitely no. Because buddhā said in Sutta. Saṃ. Sa. Dvādasamaṃ āḷavakasuttaṃ:

(The Blessed One:)

“With faith you cross the flood

and with diligence the ocean
With effort end unpleasantness
and with wisdom purify yourself.”

Thinking that with death and the break up of the body of a Realized One that some real thing utterly ends contradicts the doctrine of anatta and was specifically refuted in Pali Canon Sutta.

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Are either of the two truths Truths (Satya)?
Is it reasonable to call these truths, or would it be more reasonable to call them accurate statements from two different frames of reference?
The truth, from the frame of reference of conditioned experience, is emptiness.
The truth, from the frame of reference of the unconditioned, is neither the condition of emptiness, nor the condition of non-emptiness, neither both nor neither.
.. In that a statement with regards to the ultimate is false from a conditioned frame, and a statement with regards to the conditioned is false from the ultimate frame, how can either one declare any 'satya'?

Generally speaking, I agree with you, they are more like descriptions from two different standpoints. But I would actually go further and don't even call them "accurate". In my mind, they are just approximations pointing in a certain direction, and when I blend both, I get a sort of 3D-vision in which I see reality as is. This reality is a lot more "real" than these two flat projections, and they can't even come close to capturing it in all its awesome depth.

Prasangika-Madhyamika define a truth as whatever is not deceptive in that it appears the way it exists. The opposite of a truth is a falsity.
Ngawang Palden says:

Ultimate truths necessarily are established in accordance with how
  they appear to the awarenesses to which they clearly appear.
Conventional truths are necessarily falsities. The meaning of falsity
  is “deceptive,” and the meaning of deceptive is “discordance between
  the mode of appearance and the mode of abiding.”

Ultimate truths are truths because, in the perspective of the wisdom directly realizing them, they appear the way they exist (i.e. empty). On the other hand, conventional truths are falsities and not truths because they appear as inherently existent while they do not exist in this way. Thus, conventional truths are truths only in relation to ignorance. This is because ignorance conceive of them to exist the way they appear.
In Tsong-kha-pa’s Final Exposition of Wisdom by Jeffrey Hopkins, it says:

In saṃvṛtisatya, saṃvṛti means that which obscures, or conceals,
  reality, and thus saṃvṛtisatya means "that which is a truth for
  ignorance".

Maybe what Plato described is close to what's happening.

The truth, from the frame of reference of conditioned experience, is emptiness.

Yes, for the people in the cave what is there is just the shadow and it is really empty.

The truth, from the frame of reference of the unconditioned, is
  neither the condition of emptiness nor the condition of
  non-emptiness, neither both nor neither.

For the one outside the cave, when asked by those in the cave to describe what is ultimately real using the shadows and echoes of shadows his answer can only be neither nor...
For those in the cave, it's true that the horse is 10ft tall, and the ultimate truth that it's 4 ft is not true for the cave dwellers.


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After months of daily meditation I can't concentrate
I'm doubting if I will be able. Not even a single breath my mind stop talking. I start with metta and try to sit for at least half an hour to an hour a day. I don't skip even a single day. It's a huge effort and I am starting to feel disappointed.

Which type or types of meditation do you practice?

I attended two vipassana retreats of ten days, where I learned metta anapana and vipassana. But at home I have been doing mainly anapana and metta because I thought I needed to be able to concentrate on breathing at least a bit to then start vipassana. But it's just not getting any better.

Possible duplicate of Inferiority because of failure in meditation

I think you try too hard to get, to achieve a calm mind. It will settle on its own if you don't try but relax with the breath, with the body. Just let things be without trying to control. Come back to breath gently and calmly when you catch yourself caught in thought.  Be kind to yourself, patient with yourself as you would with a good friend. Each time the meditation will be different. Come with curiosity and openness to the sitting. How it will be this time?

While similar in nature, I don't think the two questions necessarily are duplicates. This question revolves more around samatha meditation. I think we should let it stay open.

I feel concentration is often misunderstood, perhaps because it was by me for a long time. Perhaps you could think of it more as awareness than concentration.

There are several things I would advise:

Start with your body. Change your attention from "life" to feelings in your body: tensions, emotions, energies etc. Reconnect with the parts you've not been paying attention to. Feet are often completely forgotten. Relearn to feel everything, first part by part, then all of your body at once. Relax all tensions, sometimes there may be tensions in abdomen that take years to relax, just sit & watch it and trust your intuition/feelings which part needs your attention.
Make a very careful study of your breathing. Breathing is always connected with emotions. Short, long, calm, nervous, blocked, there are millions, no - billions - details in the breathing. If you watch your breathing muscles, particularly diaphragm but really chest, shoulders, abdomen, and everything else, you can "read" your subconscious mind like a book. Then start relaxing breathing, no need to force it to be slow or calm, just watch for blockages and remove them. Just remove them one by one. This may take days and days, but eventually you should be able to achieve breathing that is very smooth, very subtle - and your mind will be the same, because by relaxing your breathing you're healing your mind.
If your mind is chatting, pay attention to your mouth muscles: tongue, lips etc. They sometimes have the habit of moving very slightly and "saying" things (this is called "subvocalizing"). Try relaxing the mouth muscles by feeling how tired they are from constant work. If this does not work, try reading a mantra - any mantra that you like and that makes you feel good - it should help wash out habitual talking. In worst cases this may take a long time, up to a year.
Finally, no need to worry so much about "concentration". Women's mind is different from men's (not better or worse, just different). Women's mind is naturally wide open, while men's mind loves to box itself. No need to box it. Just sit and stay open. The more open you get, the less fight there is inside you, the fewer thoughts and images will your brain generate. The metaphor for this is lion's gaze (unlike dog's gaze). Dog's gaze follows the objects, while lion's gaze just stares at everything, ready to jump. Be like a lion, strong, confident. It's a mood you can generate: bright, strong. Don't worry about thoughts, focus on the mood. Thoughts come and go but the lion stays in place, with its majestic presence.

Very helpful answer. 1 question. If you watch your breathing muscles, particularly diaphragm but really chest, shoulders, abdomen, and everything else, you can "read" your subconscious mind like a book. Do shoulders, abdomen breath? I didn't get the sentence. Do you mean to watch sensations there while breathing?

In my experience, shoulders and abdomen participate in breathing by shaping the chest & lungs and conditioning the lower ribs and the diaphragm. Ah, I see - no I did not mean "the muscles are breathing", I meant, "the muscles used for breathing" :)))

First of all, keep in mind that lay life is not conducive for high proficiency in concentration, so, be patient with yourself.
Inability in concentration means that the mind is under influence of counterproductive tendencies rooted in it, which may be:
craving for gratification through the six senses (remember that mind is a sense media too), restlessness, worry, ill-will, aversion, resentment, negativity, annoyance, boredom, tiredness, drownsiness, doubt.
In summary, whatever mind state which prevent you to be content and satisfied in the the present moment (independent of external circumstances) is a hindrance (and this include your craving for attain concentration as well). The cause for the presence of those hindrances are related to how you live your daily life: Pursing and indulging in those sense experiences which you like or trying to run away or destroy those you dislike. So, first you have to weaken (and eventually extinguish) the unwholesome latent tendencies of the mind.
Practice "mindfulness immersed in the body" (see Kaygatasati sutta and Satipatthana sutta) during your daily life.
Be always mindful, do not let yourself be carried away in the agreeable aspect of the sense experiences, attend to it as a whole, turn your attention to their drawbacks, see how shallow, brief, unsatisfactory it is and as you crave for these experiences, it causes tension, discontentment and uncertainty ruining your peace of mind. A good simile used by the Buddha to illustrate the pursue of gratification through the sense medias:

MN 54
"Suppose a dog, overcome with weakness & hunger, were to come across a
  slaughterhouse, and there a dexterous butcher or butcher's apprentice
  were to fling him a chain of bones — thoroughly scraped, without any
  flesh, smeared with blood. What do you think: Would the dog, gnawing
  on that chain of bones — thoroughly scraped, without any flesh,
  smeared with blood — appease its weakness & hunger?"
"No, lord. And why is that? Because the chain of bones is thoroughly
  scraped, without any flesh, & smeared with blood. The dog would get
  nothing but its share of weariness & vexation."
"In the same way, householder, a disciple of the noble ones considers
  this point: 'The Blessed One has compared sensuality to a chain of
  bones, of much stress, much despair, & greater drawbacks.' Seeing this
  with right discernment, as it actually is, then avoiding the
  equanimity coming from multiplicity, dependent on multiplicity, he
  develops the equanimity coming from singleness, dependent on
  singleness, where sustenance/clinging for the baits of the world
  ceases without trace."

And how to uproot those counterproductive latent tendencies:

AN 9.41
"[Buddha]: Even I myself, before my Awakening, when I was still an
  unawakened Bodhisatta, thought: 'Renunciation is good. Seclusion is
  good.' But my heart didn't leap up at renunciation, didn't grow
  confident, steadfast, or firm, seeing it as peace. The thought
  occurred to me: 'What is the cause, what is the reason, why my heart
  doesn't leap up at renunciation, doesn't grow confident, steadfast, or
  firm, seeing it as peace?' Then the thought occurred to me: 'I haven't
  seen the drawback of sensual pleasures; I haven't pursued [that
  theme]. I haven't understood the reward of renunciation; I haven't
  familiarized myself with it. That's why my heart doesn't leap up at
  renunciation, doesn't grow confident, steadfast, or firm, seeing it as
  peace."

Remember that this is meditation as well and has to be done repetitively in order to weaken the hindrances. Always use the Four Noble Truths as guidelines to evaluate your current mind state:

Stress is to be investigated
The cause of stress (craving) is to be abandoned
The cease of stress (with abandonement of craving) is to be realized
The path (Noble Eightfold Path) leading to the complete cessation of
stress is to be developed

Alongside, be virtuous, be generous, pratice metta indiscriminately, cultivate genuine interest for the welfare of all beings. Goodwill (metta) is the healthiest nutrient for the mind because doesn't have drawbacks and support concentration. Enventually, you will learn to be in a agreeable mood without relaying in external circumstances and then concentration will happen naturally.

Based on your meditation background and current focus, it appears that perhaps you have cast your net too far to catch the kind of fish that you are looking for.
As juvenile as this may seem, I stayed with guided meditation for some time before progressing further to a primarily breath based focus. Two helps: for guided meditation, I used and still use at times the “Insight Timer” app. Not only does it have the meditations, but also a timer for solo timed meditation, and groups that one can join of varied meditational topics for ideas and support, inspiration, motivation, etc. The second helper is  YouTube video talks/Facebook groups and books of Thanissaro Bhikkhu. He makes breathing meditation interesting, “easy”,  and above all his style is light but enlightening.
I used analogy on another group to which I belong which may also be beneficial here. This though in terms of keeping the mind focused, free from chatter. If it ever truly gets that way.
One takes an aspirin for a headache. The ache does not subside instantly, it takes time for the medicine to work. And, when one aspirin doesn’t do the job, it may take another to relieve the pain.
Point is, keep at it. Over time you will be successful. It takes some longer than others. You will make it!

"Not even a single breath my mind stop talking"

This the Anatta nature of the mind. This shows you that the mind is neither you nor yours.

It's a huge effort and I am starting to feel disappointed

This is the Dukkha nature of the mind. It's uncontrollable, unpredictable, impermanent and wanting to make it behave in a certain way causes suffering.
So why don't you stop trying to control the mind and try to gain some wisdom by simply observing what is happening instead of trying to make things happen?

Comments are not for extended discussion; this conversation has been moved to chat.

You actually ARE concentrating -- People mistakenly believe that to meditate is to calm the mind. That is actually not the object of meditation at all (although it may be the result down the road after a lot of practice).
The object of meditation is to notice when your mind is wandering or "thinking".....which you are obviously doing! That part of your brain that notices your mind has wandered is the part of the brain you exercise each time you notice.
Our brains all tend to run wild creating a lot of noise in our heads- but it's a different area of the brain that is aware your mind is "thinking" (almost like there are two of you in there).
Meditation is basically when you focus on something, you notice your mind wandered, you bring yourself back to whatever your focus was. That part of your brain that notices is getting a little workout - like lifting weights.
So the more you notice your mind wandering, the more of a workout your brain is getting. Being "bad" at meditation is good!
As the gray matter there thickens and becomes stronger (from noticing your mind wandered), you will find more impulse control, more self awareness, focus, concentration, ability to distinguish the actual truth of who you are, versus that noisy thinker who is filling your mind with nonsense about who you are.
Rather than trying to calm the mind, just try to notice where it's run off to and bring it back -- without judgment.
Don't worry, you are a very successful meditator!


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Karmic remnants after advice
If you gave someone good or bad advice or wrote a book that was stored in the Library of Congress and read for centuries then wouldnt you have a karmic remnant to bear?

Yes, Kauva Aatma, for a good, a bad or neither good or bad. Something most are not aware, talking "I know" and do not.
To make it short, best is it to compair it with a pit-fall. As long as it is not removed, if one actually get's trapped, the action is full filled.
Now think of how many debts some accumulate, debts keeping them to come back again and again... think on how much remorse might follow, once finding out a better.
One question, bringing that to awarness was: Pitfalls of answers: what are effects of answers having be received, yet knowing they where …. Nyom Chris gave some practical advices.
Here as a sample directly, indirectly on this matter for understanding:

For instance, if a bhikkhu harboring this sort of general intention builds a trap but then changes his mind, he has to destroy the trap so thoroughly that it cannot be reassembled. Similarly, when a bhikkhu writes a passage describing the advantages of dying (see below) with the thought that anyone who reads it might decide to commit suicide, if he then changes his mind he has to destroy the writing so thoroughly that it cannot be pieced together. If, instead of writing the passage himself, he simply picks up a pre-existing written passage of this sort and then — with a similar intention — puts it in a place where it might be easily seen, he can avoid any penalty simply by returning the passage to the place where he found it.

On effects of approve and encouragement by speech (eg. signs, gesture, letter) see also:
AN 4.83: Avannaraha Sutta - Dispraise and 6. Acelakavaggo AN03.157-163.
And that is why if is said:

"Those who point out wrong Dhamma as Dhamma, Bhikkhus, those Bhikkhus archive harm for many people, suffering for many people, for the sorrow and suffering of heavenly and human beings. Much demerits, those produce, for the disappearing of the true Dhamma. This for the thirty third.

"Those who point out Dhamma as wrong Dhamma, those archive harm for many people, suffering for many people, for the sorrow and suffering of heavenly and human beings. Much demerits, those produce, for the disappearing of the true Dhamma. This for the thirty forth.

132-139. "Those who point out wrong Vinaya as Vinaya[2]... Vinaya as wrong Vinaya... not declared by the Tathagāta as declared by the Tathagāta... declared by the Tathagāta as not declared by the Tathagāta... not practised by the Tathagāta as practised by the Tathagāta... practised by the Tathagāta as not practised by the Tathagāta... not made know by the Tathagāta as made know by the Tathagāta... made know by the Tathagāta as not made know by the Tathagāta, those archive harm for many people, suffering for many people, for the sorrow and suffering of heavenly and human beings. Much demerits, those produce, for the disappearing of the true Dhamma. This for the forty second.

And not just for one and now... long time for one to wander on having overestimate one self, not to speak on deliberately account.
[Note: This is a gift of Dhamma and not meant for commercial purpose or other low wordily gains by means of trade and exchange.]

Karma is intention. So, it depends if the person bears in his/her heart the honest wish for the benefit or prejudice of the others. And Later, if he/she recollect and rejoice in the past deed and the repercuition, this generate karma as well.


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Tatramajjhattatā • Equanimity • In the middle of all that
Friends, could anybody direct me to some suttas of the pâli canon about Tatramajjhattatā, the developed form of the equanimous abiding 'in the middle of all that'.
To the best of my knowledge, this specific mental factor is mentioned in the Abhiddhamma and the Visuddhimagga, but I was unable to find it referred to in the Pali Canon.
Many thanks for your much appreciated help, with Mettā

I don't think it is mentioned in Pali Canon, it seems the term was coined by Buddhaghosha. Do you mind providing quotes from Abh and Vsm? What this reminds me though is ataraxia of Pyrrho, which was supposedly a concept he picked up from Buddhists in Northern India. ("In non-philosophical usage, the term was used to describe the ideal mental state for soldiers entering battle.") I wonder if Sarvastivadins had a similar concept... Perhaps Tattvasiddhi-Śāstra has something on the topic...

I think I heard these texts being mentioned in that talk : https://www.abhayagiri.org/talks/6179-in-the-middle-about-that but I fear I may be unable to provide specific quotes.

Upekkhā word is used in 10 contexts of suttanta with 10 meaning, which were analysed by sāriputta-aggasāvaka, then concluded to 4 sabhāva:

One refers to vedanā (upekkhā-feeling).
One refers to viriya (effort).
Two refer to paññā (understanding).
Six refer to tatramajjhattatā (equality/parity/counterbalance).

So, when sāriputta try to explain each upekkhā, he used the synonym words to explain them, like we saw in the dictionary, nowadays, such as in KN. Jūlaniddesa, Udayamāṇavakapañhāniddeso:

[446]    Upekkhāsatisaṃsuddhanti   upekkhāti   yā   catutthajjhāne
  upekkhā   upekkhanā   ajjhupekkhanā   cittasamatho   cittappasādatā majjhattatā   cittassa.

That is the original tatramajjhattatā in pāli cannon.
Why commentary concluded 10 meaning to 4 sabhāva?
Because of the main topic of each contexts, which each upekkhā word appearing. For the example in SN Mahāvagga, First Ānandasutta:

[1393]   Yasmiṃ   samaye   ānanda   bhikkhu  tathā  samāhitaṃ  cittaṃ
  sādhukaṃ    ajjhupekkhitā    hoti   upekkhāsambojjhaṅgo   tasmiṃ   samaye
  bhikkhuno   āraddho   hoti   upekkhāsambojjhaṅgaṃ   tasmiṃ   samaye  bhikkhu
  Bhāveti   upekkhāsambojjhaṅgo   tasmiṃ   samaye  bhikkhuno  bhāvanāpāripūriṃ
  gacchati.

You can see sama-word and ajjhupekkhā-word, which appeared in Udayamāṇavakapañhāniddeso like tataramajjhupekkhā, explaining upekkhāsambojjhaṅgaṃ. So, commentary concluded them as the same type upekkhā, tattaramajjhupekkhā.


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Where does it say that venerable Moggallana got lost in space?
I've heard a story about venerable Moggallana (after he became enlightened). Moggallana, the left chief disciple of the Buddha, got lost in space when he tried to find the limits of the universe. Then when he was about to give up on life, the Buddha sent his aura(a beam of light) to show venerable Moggallana the way back to earth. Anyone has a reference to this story?

Did Tathagata find the end of universe?

@Rajas. There is no conceivable end.

Tathagata did find end of the world, where elements have no footing but not by travelling. " ‘Bhikkhus, I say that the end of the world cannot be known, seen, or reached by travelling. Yet, bhikkhus, I also say that without reaching the end of the world there is no making an end to suffering,’"

Saṃyutta Nikāya 35,116. Going to the End of the World

@Inb4dead didn't find the verse

https://suttacentral.net/en/sn35.116

It is just a fable. It is not come from the ancient theravada pali cannon, both tipitaka and commentary. Because in Thailand we have many translated pali cannons, included those both, but no one found this fable in any cannon.
However, it maybe derived from SN Sagāthavagga, rohitassasutta, and KN Jātaka, javanahaṅsajātaka's commentary, which bodhisatta had helped the past life of moggallana.

i'm  aware of the Rohitassa sutta. But this story is not connected to that.

I added some more source, above.

No it's not a Jataka story. It's something that said to have happened during time of the Buddha after venerable Moggallana became the foremost in magical powers.

This story occurs in chapter 40 (kindred sayings about moggallana) of the Salayatana-vagga, which is the fourth book of the Samyutta-nikaya (book of kindred sayings).
The relevant passage, (section 5, entitled ‘space’) can be summed-up as follows:

(Then I thought, friends) : “They say, ‘The realm of infinite space, the realm of infinite space.’ Now what is the realm of infinite space?’
Then, friends, this occurred to me: Herein a brother, passing utterly beyond the perception of objects, by the coming to an end of the perception of resistance, by not attending to perception of diversity, with the idea of “infinite is space,” enters on and abides in the realm of infinite space. This is called “ the realm of infinite space.”
So I, friends, passing utterly beyond the perception of objects . . . entered on and abode in the realm of infinite space.
But when I had thus abode (and had emerged from trance), perception and work of mind, connected with the perception of objects, still continued.
Thereupon, friends, the Exalted One by magic power came to me and said: “Moggallana, Moggallana, be not remiss in the realm of infinite space, brahmin ! **Make steadfast the mind, make the mind one-pointed, compose the mind in the realm of infinite space.”
So after that, friends, passing utterly beyond objects . . . I entered on and abode in the realm of infinite space.
Now, friends, if any would rightly say: “Helped by the Master the disciple won great super-knowledge,” of me would he rightly say: “Helped by the Master did the disciple win great super-knowledge.”’
Translation by Mrs. Rhys Davids.
Source

Nice! But that is about meditation and it is before venerable Moggallana became enlightened.

I don't understand your comment. First of all, are you looking for sources regarding Moggallana, AFTER he became enlightened? If so please mention this in your question. Second, does it matter that this story regards meditation, when one considers that the phrase "getting lost in space" doesn't necessarily restricts to the context of one's own mental sphere? If you are looking for specific answers, please mention in your question.

Well, it is not about meditation. It was about him travelling through space using magical powers and it is said to have happened after he became enlightened. Now you know :)

I still don't fully understand the context. If he was already enlightenend, then why came that "he was about to give up on life"? And secondly, by saying "the way back to earth" you mean that he was present on the earth in an enlightened form?

Approved your edit. No, he physically travelled. Give up on life as in deciding to stop using his magical powers to sustain life in space as he didn't know the  way back to earth.

This also appears in the Amitabha Sutra commentaries:
Once when Sakyamuni Buddha was teaching the Dharma, [he told his disciples that] his voice could be heard many distant lands away and that the force of his voice could be felt in many worlds. One of the Buddha's disciples, Maudgalyayana, who was the foremost in supernatural power, was skeptical that the Buddha's voice could reach such far-off places. He decided to investigate for himself and used his supernatural power to go to a Buddha Land that was ten billion Buddha Lands away. In this Buddha Land, Tathagata Lokesvaraja was preaching the Dharma. At this particular moment, a person in the audience picked up something on his body and exclaimed, "Why is a little worm crawling on my body?"
Tathagata Lokesvaraja said, "This is not a little worm; this is Maudgalyayana, a disciple of Sakyamuni Buddha from the saha world." Actu-ally, Maudgalyayana was not small; it was just when compared with the people of this Buddha Land, he was no bigger than a little worm. Then Tathagata Lokesvaraja told Maudgalyayana, "The eminence and virtues of all Buddhas are not something that can be comprehended and equaled by sravakas. You should not test them with your supernatural power." From then on, Maudgalyayana firmly believed that there are limitless worlds and limitless Buddhas in the vast immenseness of space

This is Mahayana. I'm looking for a Theravada source.