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If there is no soul, how can there be rebirth?
Anatta is often described as "not-self" which I understand to mean that our identities are illusions.  But it's also described as "soullessness" which I think implies that there is no mind other than the brain itself.
But many Buddhists believe in rebirth.  If there is no soul, how can there be rebirth?

Thank you all for the considered and learned answers. I shall study the texts in question. However, I am a simple man. Is there a simple answer to my question? Thanks and best wishes.

see https://tricycle.org/trikedaily/rebirth-debate/
"His main concern, however, was not whether there is or is not life after death, but whether it is possible to live in such a way that one could transcend the dilemma of suffering."

I've read of rebirth as the transmission of 'impressions'. I like this way of describing it. It suggest a medium for transmission but not a 'thing' that is transmitted.

The absence of a soul is not declared by Buddha. In MN 63, Buddha himself has said, "And what is undeclared by me?..The soul & the body are the same'... 'The soul is one thing and the body another' is undeclared by me.

When most people think of "self" they think of some abstract core that is the subject of all experience and the agent of all actions. Buddha taught (and modern cognitive science tends to agree) that upon careful examination there is no such single core. Instead experiences result from interactions of multiple perceptory functions. Similarly, our actions are performed by a conglomerate of functions, without a single agent responsible for all choices.
When the notion of individual rebirth exists as an unexamined belief, it depends on this unexamined notion of "self" as its necessary foundation. Once practitioner is free from illusion of self (in practice, not just conceptually), the notion of individual birth/death/rebirth no longer applies. From this perspective, rebirth is a byproduct of attachment to a (substantial) self.
But because karma at large still continues to function, the infinitely forking/joining threads of causation that once were the subject of attachment continue to participate in activity and serve as causes for subsequent effects. In this sense, rebirth as principle goes on continuously whether we posit an individual or not.
To give this a more practical spin, instead of worrying about rebirth, we practitioners should focus on working towards deconstruction of self by reducing the strength of the illusion through practice of altruism and non-attachment, first and foremost at the microscopic level of thought-to-thought intention and reaction.

n.. Once practitioner is free from illusion of self (in practice, not just conceptually), the notion of individual birth/death/rebirth no longer applies. From this perspective, rebirth is a byproduct of attachment to a (substantial) self. Influenced me.

So if I understand you correctly, there is no such thing as rebirth of self or rebirth of the individual, just ongoing causation.  Is this an accepted position among practitioners?

Chogyam Trungpa Rinpoche, when asked what is it that gets reincarnated said "neurosis". He was joking of course, but seriously, it is nothing else but Karma or we could say information. You can ask around but yes, I believe this is a common understanding among advanced practitioners

@AndreiVolkov In my reasoning, the following sentence strengthens the independent existence of a self: working towards deconstruction of self. It implies the deconstructed self is there the moment you are not working on its deconstruction, which is not true. There is no self to begin with, hence there is nothing to deconstruct. It is rather learning to see that you are constructing it, and when fully seen that you are, it is simply a matter of not having to put it together anymore, as reality is easier worked with without that delusional mental construct.

I agree with many of your assertions here, but I still hold that illusion does not have to be reality in order to be functional and require deconstruction.

I understood it the same way, but then what past lives have Buddha been talking about? How could he get access to memories of past lives, if there are no past lives, that could be considered "his"? And what are teachers talking about when they say that "you" might be able to achieve nirvana in the next lives, if not this one? Those will not be your lives anymore. Either you liberate yourself in this life, or generate further suffering for next lives, which will have to try to liberate themselves from in their life.

Buddha talks about "spirit" in Pali Canon. Spirit is soul without body. See Ratana sutta, Aja Sutta, (in many more Suttas, also in Jataka tales). Search word "spirit" in accesstoinsight. End of topic.

Anatta is often described as "not-self" which I understand to mean that our identities are illusions.

No, in fact, the meaning of not-self, as others have pointed out, is that the object in question is not self :) The Visuddhimagga offers some good explanations:

All that [materiality] is “not-self in the sense of
  having no core.” In the sense of having no core because of the absence of any core of self conceived as a self, an abider, a doer, an experiencer, one who is his own master; for what is impermanent is painful (S III 82), and it is impossible to escape the impermanence, or the rise and fall and oppression, of self, so how could it have the state of a doer, and so on? Hence it is said, “Bhikkhus, were materiality self, it would not lead to affliction” (S III 66), and so on. So this is also not-self in the sense of having no core. Accordingly, there is one kind of comprehension in this way too, but it is effected in eleven ways. [611] The same method applies to feeling, and so on.

and

There are twenty-five kinds of contemplation of not-self by taking the following five in the case of each aggregate: as alien, as empty, as vain, as void, as not-self.

You say:

But it's also described as "soullessness" which I think implies that there is no mind other than the brain itself.

Absolutely not! The five aggregates are non-self, four of which are outside of the domain of the brain.

If there is no soul, how can there be rebirth?

There isn't in fact any such thing as rebirth, in ultimate reality. Nothing is truly reborn, ever. Every experience that is made up of the five aggregates arises and ceases without remainder. That is true death. Rebirth is a concept used to describe the change between one artificial framework of experiences (e.g. a human life) to another. The ultimate reality is that the mind simply arises and ceases at the last moment of life and then a new mind arises at the first moment of rebirth based on the last one, very similar to as has been occurring throughout one's life, except this time there is no old physical phenomena for it to be based on, so it is based solely on one's final state of mind in the last life.
Here's something that might help:
https://www.youtube.com/watch?v=XClIR19eufc

+1 Excellent elucidation! I have a query here though: "Nothing is truly reborn, ever. Every experience that is made up of the five aggregates arises and ceases without remainder.": If that is the case, then how can one remember the past lives (Buddha did as mentioned in the sutras and Jataka tales)? The fact that he remembered clearly demonstrates a link between this and past life. If there is no self, then what is that link?

@PrahladYeri Think of it as a mango tree retaining the qualities of the mother tree without retaining any cell of the mother tree.

The principle of not-self is not saying "No self", it's saying a specific kind of thing:

"Bhikkhus, feeling is not-self...
"Bhikkhus, perception is not-self...
etc.

From Anatta-lakkhana Sutta: The Discourse on the Not-self Characteristic
Upon the greater question of "does some kind of self other than the aggregates exist", the Buddha refused to answer:

"Malunkyaputta, did I ever say to you, 'Come, Malunkyaputta, live the holy life under me,
and I will declare to you that...
'The soul & the body are the same,' or 'The soul is one thing and the body another,'...
"No, lord."
"And did you ever say to me, 'Lord, I will live the holy life under the Blessed One
and [in return] he will declare to me that...
'The soul & the body are the same,' or 'The soul is one thing and the body another,'...
"No, lord."
...
"So, Malunkyaputta, remember what is undeclared by me as undeclared,
and what is declared by me as declared.
And what is undeclared by me?...
'The soul is one thing and the body another'

From Cula-Malunkyovada Sutta: The Shorter Instructions to Malunkya
He says "when there is the view, 'The soul is one thing and the body another,' there is still the birth, there is the aging, there is the death, there is the sorrow, lamentation, pain, despair, & distress whose destruction I make known right in the here & now."

The answer might be in: "Thus, Ananda, from name-and-form as a requisite condition comes consciousness. From consciousness as a requisite condition comes name-and-form..." - Think of it.
Maha-nidana Sutta DN 15

First, you need to understand that Buddhist texts operate on two levels of description: the conventional truth and the ultimate truth. The contradiction disappears when you realise that anatta (the non-existence of self) is an ultimate truth, while the rebirth is a conventional truth.
In other words, Buddhists believe that people linked by a chain of rebirths may be said to be "the same", by the same convention as when a 40-year-old person is said to be "the same" as an 20-years-old person he evolved from. This convention has nothing to do with the fact that there is no indivisible and constant "I", and that the aggregates that make up the conventional "I" are in constant flux.

This analogy (your second paragraph) made the most sense to me. Thank you.

The "answer" seems to be more like a glass of water being taken from a river and then being  poured back into the river. Can the exact same glass of water ever be drawn from that river? Possibly, but extremely improbable, but another glass of water may be drawn from the river, a river that has been influenced by the actions of the first glass of water. Analogies never take in all angles but I like this one.

This is my favorite analogy overall. Others have used it also. I have read that the Buddha said, "Tendencies persist, but not a self" but I cannot find it on the web to provide a link. Perhaps someone else knows how to locate it.

A new analogy for me, and I love it! Thank you!

This is a question of kings! Many many years ago, a king asked the same question of a monk. Here is the dialogue from Sutta Central

The king said: ‘Where there is no transmigration, Nāgasena, can there be rebirth?’
‘Yes, there can.’
‘But how can that be? Give me an illustration.’
‘Suppose a man, O king, were to light a lamp from another lamp, can it be said that the one transmigrates from, or to, the other?’
‘Certainly not.’
‘Just so, great king, is rebirth without transmigration.’
‘Give me a further illustration.’
‘Do you recollect, great king, having learnt, when you were a boy, some verse or other from your teacher?’
‘Yes, I recollect that.’
‘Well then, did that verse transmigrate from your teacher?’
‘Certainly not.’
‘Just so, great king, is rebirth without transmigration.’
‘Very good, Nāgasena!’

Those are metaphors, but what actually passes from life to life? Habits! All we have to do is break the habit of wrong desire. Here is another reference: sutta central where habits of wrong desire are compared to feeding the oil-lamp.

In original Pali Buddhism, there are two levels of teaching: (i) mundane, for the purpose of nurturing morality; and (ii) supramundane, for the purpose of enlightenment (MN 117; MN 60). The teachings that imply 'rebirth' are mundane & the teachings that explain 'anatta' are supramundane. If we carefully read the many Pali suttas, we will not find 'rebirth' & 'anatta' in the same sutta. They are two distinct topics for two distinct audiences.
For example, MN 60 states the view of 'self' or 'existence' is right view for householders but SN 12.15 states the view of 'self' or 'existence' is not right view.
The word 'birth' ('jati') refers to the birth of the idea of 'self-identity' ('sakkaya' - MN 44) or 'persons/beings' ('satta' - SN 12.2; SN 23.2; SN 5.10; SN 22.81). Minds that are not enlightened are subject to 'rebirth' of the deluded 'self-view' each time they cling to an act of karma. Minds that are enlightened have ended 'birth' & have ended clinging karma (AN 6.63).
Because the old Pali suttas do not mention anything that is 'reborn' from life to life, the later Buddhists were required to invent what they call 'relinking consciousness', 'storehouse consciousness', 'stream of consciousness', etc, which are ideas the original suttas did not teach. The original suttas only state consciousness is the six-fold cognition (MN 43) and there can be no arising of consciousness without sense organs (MN 38) and aggregates (SN 22.53; SN 12.67).

There is no rebirth / reincarnation (in the sense that the soul takes on a new body after the death of the previous body. )
Our existence is changing process in which there are events like birth and death. In the absence of a unchanging everlasting core the person who is born is not the same as the person who died nor is he a deferent person but but just the continuation of the process of existence.
In Buddhism what is there is Jati /  birth and death as events in the process keeping us in the cycle of Samsara.
There is no continuity of the person (or some core identity / entity) but there is a continuation of the process.

Only "eternal, unchangeable, and happy" Soul (which is called atman) is denied in Buddhism. And such monistic Soul is not required for re-birth to function. When being disintegrate it is causally condition birth of new being. Thus, even though there is no constant Soul, two beings are related to each other causally by means of karma. So, instead of Soul (and re-incarnation) we have Karma (and re-birth).

The Pali word 'atta' is generally translated as 'self, body, person, individuality; life, mind-soul.' As the PED makes clear, the Buddha is alluding to a very specific concept - the Upanishadic idea of a substantial being that inhabits the heart that is reborn from life to life and is inherently permanent, self-identical, and blissful. The Buddha points out that no amount of observation can confirm the existence of such a being. Instead, he posits a continuity of moments, each moment infintesimal and non-substantial, which he calls the 'santana,' generally translated as 'continuity, succession,' often referred to as the 'mind-stream.' The difference between the 'atta' and the 'santana' is that the former is substantial and static, whereas the latter is non-substantial and dynamic. The 'santana' manifests in samsara as a consecution of states resulting from unfruited karma, which in turn arises because of objectification due to ignorance (avijja). However, when all karmas are eliminated there is "that which remains," which continues to be non-substantial and dynamic. This is the Deathless (amara, same root as amrita). The Buddha clearly rejected nihilism, he refers often to the attainment of immortality and refers to the "self" as frequently as he denies its existence. The notion that the Buddha denied the existence of a self in any sense is naive, and is easily disproved. When the Buddha attained Enlightenment, only the Buddha became enlightened, nor did the Buddha himself disappear. This proves the existence of the individuality, the essence of which is intention (cetana), the primary characteristic of which is 'not-knowing' (avijja). This is a primary aspect of reality itself, one polarity of the transdual absolute of which the opposite polarity is emptiness or void (shunyata). What the Buddha rejected is the doctrine of a being inhabiting the heart with the characteristics described. In other words, he is opposing the objectification of the santana as a static object. It is the process view of reality (cf. Whitehead's Process and Reality). Esoterically, we may say that the ATTA is the A-TA, the "not-that." See also the Dalai Lama, Buddha Nature.

When I first read this, I liked what it said, but then I wasn't sure sure how/whether it answered the OP's question. I.e., I can see you address the "no soul" part of the question, but what about "rebirth"? I suppose there's connection between "rebirth" and santana, if so could you perhaps try to clarify that slightly or be just a little more explicit about it? Thanks.

Rebirth is not the rebirth of a thing, but a continuity of karmic causes and effects.

Think of exchanging the terms.  If there is no rebirth how can there be a soul.  Attachment will be there both ways.  Why must one condition rely on another.  Why must a soul be present for a rebirth ?  Why must there be a rebirth to validate a soul.  Soul is a category based on a disposition masking itself as a representation.  You are not a soul.  You are not a rebirth.  You are not a name.  You are not a species.  You are not a category.  You are not a self.  You are not a hope to be.  You are not a never was.  You are a system of directed energies subjected to and affected by other directed energies.  All religions and convictions are merely reminders and reinforcers of how we are to be.  Like signs on the road.  How do you direct your energy ?  Will believing you have a soul help you in redirecting your energy ?  I do not know this .

If there is no soul, how can there be rebirth?

I think this is a very important question and one which really gets to the heart of a big misconception about emptiness or the selflessness of persons.
To my mind, the best way to see the hidden assumption in the question above is to ask another question: why invoke rebirth?
How about this alternate question: If there is no soul, how can there be a person who lives moment to moment?
It is clear, that all schools of Buddhism teach the selflessness of persons. This is one of the four seals of Buddhism. So, why don't we ask how can there be a person who lives moment to moment?
It's manifestly evident that people live moment to moment. With just a little bit of insight we can see that persons are impermanent. That we are  non-unitary (we have parts). That we are dependent phenomena. That right there is enough to establish the selflessness of persons at a course level and yet we still function and live moment to moment.
Rebirth is simply the continuation of this living moment to moment even after the death of the body. In other words, the question has two hidden assumptions:

That selfless things can not function
That we are thoroughly material and can be reduced (physical reductionism at work) to pure matter.

The Dharma does not contain these assumptions and there are good reasons for rejecting both.

All most all above answers are helpful in getting rid of confusions regarding rebirth. Still I will say something in this regard as I think it will be an answer in quite simple words.
I am pasting my answer to other question regarding rebirth. That question also has another link. This link will take you to the original text based on which I have tried to answer.
Hopefully that answer is suitable and in very 'easy words'. -
https://buddhism.stackexchange.com/a/1846/208

with a suggestion I have copy pasted the whole ans. -
I think rebirth is part of Buddhist doctrine. But the real question is rebirth of what? and rebirth of whom?

According to the Buddha, there are four elements of Existence which go to compose the body. They are (1) Prithvi; (2) Apa; (3) Tej; and (4) Vayu. Question is, when the human body dies, what happens to these four elements? Do they also die along with dead body? According to The Buddha they join the mass of similar elements floating in (Akash) space. When the four elements from this floating mass join together, a new birth takes place. This is what the Buddha meant by rebirth, as I have understood it. It must be noted that the body dies. But the elements are ever-living. This is the kind of rebirth in which the Buddha believed. Great light is thrown upon the subject by Sariputta in his dialogue with Maha-Kotthita. The Buddha was not an absolute annihilationist. He was an annihilationist so far as soul was concerned. He was not an annihilationist so far as matter was concerned. (I think Andrei Volkov is also saying the same point when he is talking about "complete annihilation).
There is another concern here. It is about rebirth of Whom? Does the same dead person take a new birth? Did the Buddha believe in this thesis? The answer is, "Most improbable." The answer depends upon the elements of existence of the dead man meeting together and forming a new body; then the possibility of the rebirth of the same sentient being is possible. If a new body is formed after a mixture or the different elements of the different men who are dead, then there is rebirth but not the rebirth of the same sentient being. This point has been well explained by sister Khema to King Pasenadi. Where she ends up saying 'The Tathagata exists after death...exists not after death', does not apply." (Again we can match Jayantha's write up regarding Kalama Sutta.) I have drawn lot from The Buddha and His Dhamma Book 4, Part 2, section 1, sub section 2.  Hoping for further discussion.

Seed has a tendency to produce a life again. So seed contain the complex that creates new life. But when the same seed has been burnt and popped, will it return to seed again and create anew? No.
So whatever there is the condition to reappear, has the tendency of  cessation. Like popping corn.
Hence if you take seed as your self, creation continues. If you burn that seed and make into pop corn, will you still think you have soul? No.
Hence all things are impermanent, interdependent, cause of one another and no self!
Hope you will burn that seed!

I am not a Buddhist, but in reading "the Essence of Buddhism" by P. Lakshmi Nasaru, what strikes me is how the Buddha wants his followers not to accept blindly anything, but to question everything and come to realize their own conclusions. Independent thought and deep inquiry in oneself, seems to be the way of progress, not acceptance of authority. Perhaps this is the final test: after purifying consciousness through all the practices, over a long time, you finally realize you ARE an eternal soul, and then as a result, in the end, you must give up attachment to the Buddhist doctrine. Tricky, this Buddha.

There's a description of the phrase, "not me, not mine, not myself" (or "this body is not mine; this am I not; this is not my soul") which says, "With craving (tanhā) one erroneously thinks – This is mine. With pride (māna)
one thinks – This am I. With false view one thinks – This is my soul. These are
the three misconceptions (maññanā)."

@User. Actually by following the noble eightfold path you come to realize Anatta, i.e. that there is no permanent or lasting self, no experiencing or enduring entity, no inner-core.

You ARE means I AM. This is what everyone's view. No need any practice for this belief. those who have mind automatically do this. Only humans can think other way. Is the first cell is yourself.? what happen it when you Die? What are the attributes of Soul?

It's like saying there is not-self or soul so consciousness cant move forward. Consciousness throughout life,  throughout Samsara, is always dying in every fraction of a second then arising again in the next.  When consciousness arises again that is a rebirth.
Why do we assume that conciousness won't continue after physical death? Mindfulness meditation challenges those kinds of assumptions.

If there is no rebirth how will you come back to find out???
Your understanding of “soullessness” needs attention.
This is wrongview of annatta i guess

This is an excellent question. Karma is well accepted in Buddhism, but not the existence of the soul. This inconsistency raises the question of remnant reaction. Consider the following argument.
From the system of karma we know that a person who does the action will be the same person who will experience the reaction, not any one else. Suppose a person dies, then what will happen to the inexperienced remnant reactions? It can't just go away, can it? No, and we know from system of karma that the same person will born again to experience the pending reactions. So here is the question, what is common in both the persons that you say the new born one is the rebirth of the old deceased one? If the two persons are identical then there has to be something common in them, isn't it? So what is that fundamental unit that is common to both? It can't be the body, nor can it be the mind (as memory, tendencies, qualities, etc. are different). So what is the common element? The answer is soul. I have to keep it brief so can not go elaborate more but the short answer is soul exists.
Why did not Buddha acknowledge the existence of soul?
The mission and objective of Buddha was to ward of suffering of the people which is primarily caused by attachment. So He didn't acknowledge the existence of soul. But just because He didn't acknowledge its existence, it doesn't necessarily mean it doesn't exist. He didn't acknowledge the existence of soul because it will create attachment to an eternal self. And where there is attachment suffering will undoubtedly follow. During His time in India people were doing Vedic sacrifices, yanjya, rituals, etc. to place there self in heaven etc. As they believed in the eternal soul, they were attached to it and hence putting effort to place it in heaven and higher realms by animal sacrifices in yanjya and rituals. So He didn't acknowledge the existence of soul to free followers from attachment towards an eternal self.
However, if you go into more deep then you will find that the soul exists in such a way that its existence can be safely overlooked. So even if you deny the existence of the individual soul you will not be completely wrong.

Well, one constraint of SE sites is that we can't have an argument here and this really is an argumentative question. I know my answer is unacceptable by Buddhist followers, but I don't mean to say that Buddhist view regarding no soul is wrong. Hence, you are welcome to down vote the answer but think without any bias on my argument and at least leave a reason.

I will be putting a link in my answer. Plz do read it. there is no contradiction in denying separate existence to soul and at the same time professing concept of rebirth. The reading will be helpful to elaborate my point. Plz do read and comment. I also think that @ catpnosis answer also throws some light on it. But it is too short.

"But just because He didn't acknowledge its existence, it doesn't necessarily mean it doesn't exist"- Wrong, Buddha clearly said that a soul doesn't exist. What exists is only cause and effect which is explained in'dependent origination'.

In the Ananda Sutta, the Buddha states that there is no self - "If I ... were to answer that there is a self, would that be in keeping with the arising of knowledge that all phenomena are not-self?". And in the Acela Sutta, the Buddha responds to your points. Please see this answer for elaboration.

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Are there formal mechanisms in any Buddhist institutions that explicitly reconcile Buddhist principles with science?

If science proves some belief of Buddhism wrong, then Buddhism will have to change. In my view, science and Buddhism share a search for the truth and for understanding reality. By learning from science about aspects of reality where its understanding may be more advanced, I believe that Buddhism enriches its own worldview.
  -- Tenzin Gyatso, the 14th Dalai Lama in "Our Faith in Science", The New York Times

This is all very well, but are there formal mechanisms in any Buddhist institutions that explicitly allow Buddhist principles to be reconciled with the findings of science?

Not sure I can answer the question, but I am trying to understand what you're asking. Do you mean is there a similar "papal bull" mechanism to change fundamental beliefs of the religion?

It would help if you'd specify which kind of Buddhism you have in mind. Only an institution can have a formal mechanism. This implies you have some institution in mind (maybe FTMT or the Tibetan Government in exile?) Buddhism as a whole has a lot of institutions and even people like myself who go out of their way to not participate in an institution.

@matthewmartin, any kind will do.  :-)

The general claim in Buddhism, or at least in Theravada Buddhism, is that a Buddha is omniscient. That makes it difficult to question what the texts claim the Buddha himself said. In a couple of places this seems to put science and Buddhism at odds (e.g. causes of earthquakes).
The closest we have to what you are suggesting is an act of the sangha; after the Buddha passed away, we have record of a Buddhist council where they discussed whether to revoke the minor monastic rules as the Buddha had allowed them to do, and they decided as a group not to. Later sangha councils edited the canonical texts but would never have redacted something that they thought the Buddha had said in error.
I think, at the very least, unlike faith-based religions, Buddhism doesn't rely on absolute statements of truth, but rather practices that lead to self-realization; so it doesn't matter as much if statements in the canon like the causes of earthquakes and the size of the universe, etc., are accurate. What matters is if the path leads to the goal, and that is to be verified by oneself.
As a result, you find more marginalizing of problematic teachings, rather than striking them out. First of all, because the Buddha was said to be infallible, but second of all because we know that we are not. The fear of wrongly striking a teaching out of ignorance is too great. But, we can always ignore troubling passages, I guess similar to how Jewish people ignore Leviticus for the most part.
So, no, there isn't really such a mechanism, afaics.

The goal of science is most complete and accurate description of the world. The goal of Buddhism is to clearly realize relationship between mind and experienced reality and to transcend the limits of any single description of the world. So in a way, Buddhism lives in an infinity of higher order than the one science lives in. If anything, it is science that should reconcile with Buddha-Dharma, by becoming aware of inherent Emptiness of all views, not the other way around :)

That is what I would characterize as an act of faith.  Faith and science are oil and water. :-)

Just to make sure I understand what you mean, may I ask what exactly you would characterize as an act of faith?

"It is science that should reconcile..."

The notion of some assumed conflict between science and Buddhism comes from misunderstanding of Buddhism. Once you clearly see Buddhism's ground, path, and fruition, you will clearly see that Buddhism and science are not in conflict. I would go as far as to say that any scientist worth his/her salt is already a buddhist in effect (minus the raft).

Arguably science has no need to change, simply because science is already aware of "the inherent emptiness of all views" : a scientific theory arises, is modified, and may eventually cease, in dependence on causes and conditions such as experimental results that support, modify or contradict it. That's how the scientific method works.

@BrianDrummond correct, at its best, science is already Buddhism, scientific view is enlightened view. In practice however, not all scientists consistently apply Emptiness all the time, as is evident from the way they posit and argue their theories.

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What is the difference between rebirth and reincarnation?
In my readings of Buddhist commentary there is a distinction drawn between rebirth and reincarnation. But to me it is unclear what is the difference between rebirth and reincarnation--the explanations are rather abstruse. Is there a simple one-sentence explanation of this difference?

It would be great to have the precise terms in original language, that would make it much easier to answer. Can you provide them?

i downvoted the answers cos they don't say why 'reincarnation' implies a soul

now i wish i had not, but cannot reverse my vote. my question here should i hope answer the question i've posed more thoroughly

Reincarnation implies a soul that takes a body; rebirth does not, so it is preferred.
Note that neither term has a widely used cognate in the Pali texts, perhaps because the concept of "re-" anything implies the continuation of an entity. Buddhism tends to talk about birth and death in a more linear fashion; rather than being reborn, it's "being born again" (e.g. dukkhā jāti punappunaṃ).
Further, the focus in Buddhism is on individual mind states and ultimate reality rather than the conceptual reality of birth and death, so it's not really a core teaching. Death is a concept; at the moment of a being's death, one body/mind experience ceases and the next one arises, just as it did through the entire life.

The Buddhist Pali word 'birth' ('jati') refers to the arising of the self-view of 'a being' ('satta').

And what is birth? The birth of the various beings into the various orders of beings... SN 12.2
'A being,' lord. 'A being'. To what extent is one said to be 'a being'? Any desire, passion, delight or craving for form... feeling... perception... fabrications... consciousness: when one is caught up there, tied up there, one is said to be 'a being.' SN 23.3
Why now do you assume 'a being'? Have you grasped a view? Just as with an assemblage of parts, the word 'chariot' is used, when the aggregates are present, there is the verbal convention of 'a being.' SN 5.10

The many different Pali words translated as 're-birth' essentially refer to the re-arising or re-formation of the self-view of 'a being' due to kamma (action).
For example, under the influence of self-view, a person undertakes a financial scam & celebrates when they become or are 're-born' financially wealthy. Then, when they are imprisoned for fraud, the same person is re-born as a prisoner in a jail & are unhappy.
In summary, despite the different interpretations, 'rebirth' is always a doctrine of 'moral efficacy'.
Where as 'reincarnation' is always a metaphysical doctrine of the soul or some other mental substance entering a new physical body.
A Buddhist can believe in moral 'rebirth' but not believe in 'reincarnation' (life after death).

Reincarnation involves a soul that transmigrates. A soul is the five aggregates minus physical form.
Rebirth is like lighting one candle with another candle. The stream of consciousness, a.k.a life force, continues from one existence to another but the remainder of the five aggregates; form, perception, sensations and mental formations (which would stay together during a reincarnation of a soul); dissipate.

Rebirth is when a soul leaves the body in the state of ignorance and then again gets a new body in ignorance.
Reincarnation is when soul leaves the body in full knowledge and such souls reincarnate only to fulfill a some mission or purpose in life.


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Is it harmful to the Buddha when we request he or she to continue teaching instead of entering parinirvana?
One of the ten things that Bodhisattva Samathabhadra says that a person on the Bodhisattva path should do is to request the Buddhas to continuing teaching instead of entering parinirvana. Given that a Buddha is fully compassionate and omniscient, he or she would want to teach if doing so is beneficial to sentient beings and would also be aware whether teaching is indeed beneficial to sentient beings. For example, the historical Shakayumni Buddha wanted to enter parinirvana because some of his sangha was becoming complaent that they would always have  the Thus Come One as their teacher. As such, it would seem that a Buddha would be able to decide well the timing of his parinirvana.
Given the above, I wonder how would it is appropriate for one learning to walk on the Bodhisattva path to request the Buddhas to continuing teaching. Is such an action for the benefit of the practioner to generate a wish of englightment and to take refuge in the Buddha? Does a Buddha need to enter parinirvana at a certain time, otherwise it would become harmful to him or herself or to the community at large? Is a Buddha unable to stay longer to teach if practitioners do not make requests? (Sorry that I am unable to phrase a precise question, but I hope I conveyed my gist and my confusion clearly enough.)

As I pointed out in my answer to "are earthworms our mothers?"  these kind of questions often assume incorrect frame of reference. The reason we request Buddha (or our local teacher as Buddha's substitute) to continue teaching instead of entering parinirvana, is not because it can literally make Buddha (or teacher) change their mind and stay. The idea is to create a mental context in which A) the teacher feels motivated to continue teaching because he sees the teaching is in demand, B) the students stay aware of the fact that existence of the teaching in this world depends solely on Buddha and then generations of teachers passing it to one another, and now to the students, and C) the student clearly realizes that the teacher could very well leave this place but is instead making effort to stay and teach solely out of compassion for the students. When this context is established the teaching can happen effectively, because both the sides will engage actively and with no resistance.
Granted these are entry-level practices, but they are very important to establish as foundation. Otherwise what happens if you skip straight to advanced teaching, the student may get as arrogant as to metaphorically grab the teacher by the hair and swing around. Needless to say, it hurts the student first and foremost.

I'm not sure I understand your question(s) fully; however, since you seem to be coming from a Mahayana background, do remember that the Lotus Sutra reveals Buddha's entering parinirvana is merely an expedient device. He merely appears to enter parinirvana to "motivate" people, as it were. According to that Sutra, which claims to be the ultimate and true teaching of the Mahayana, the Buddha doesn't enter parinirvana but instead eternally abides in this world.

All Buddhas are masculine. No, it is not harmful to invite the Buddha. In fact, the Buddha mentioned several times that a person who has perfected Sathara Iddipada can live the maximum life span of a human at that time. It was about 120 years back then. So he could've stayed another 40 years had he been invited. Venerable Ananda had several opportunities to invite the Buddha. But it's said that Mara(the evil god) prevented him every time.


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Does studying mathematics or science lead to a practitioner of Buddhism acquiring wrong philosophical views and mental afflictions?
Among the steps needed to attain enlightenment, a practitioner of Buddhism needs to abandon the wrong philosophical views that they acquired due to either wrong teaching or wrong study. In this sense, a practitioner that is less educated need only remove his or her sense of self or ego and the afflictions due to his or her present body. However, a practitioner that is educated would also have to remove the philosophical views acquired through wrong learning.
As paradigms in science have historically been replaced by new paradigms a la Kuhn, this means that science is necessarily a wrong view. For instance, a person living in Newton's time would have studied the absoluteness of time and space, but that view was displaced by Einstein's relativistic paradigm. Whatever science we are learning now, whether it be quantum physics or evolution or species, given the historical record, would be a wrong view and replaced by a more correct paradigm in the future.
Even mathematics have proven to be contradictory through history. At first, set theorists believed in unlimited comprehension till Russell's paradox showed the need for bounded comprehension, in the fateful saga of Russel and Whitehead's Principia Mathematica. Pythagoras's theorem was thought to be unconditionally true, but now it is true in only one of the three absolute geometries and physicists now believe our world to be non-Euclidean, in which Pythagoras's theorem fails.
After one is reborn in another world, the physics or mathematics of that world would likely be very different, and one's body would also likely be very different. This probably indicates the impermanent nature of the science and mathematics of our current society.
Are you also of the opinion that the learning mathematics and science causes a person to acquire wrong views? Would this lead one further away from enlightenment?

The 14th Dali Lama's education includes logic among many subjects, including science, and is "truly interested in participating in something substantial about science"

Science and mathematics are neutral. Scientists and mathematicians, on the other hand, are not. As a fellow mathematician, all I can say is that very deep down, in the core of science, there's faith; faith in the senses, faith in matter and faith in reason. Most materialistic scientists will hide or even be unaware of this fact, but it's there. As long as you don't forget this, you'll be fine. B. Alan Wallace wrote a fantastic article about this. You can read it here.

If you are looking for enlightenment you should be concerned of not being attached to these studies, or averse to what you disagree. The same fits to Buddhism itself, you should't become absorbed, or obsessed, to the Dharma.
All philosophies are mental phenomena, they aren't either good or bad in themselves. But they can hinder your search for enlightenment if you are too concerned about them.
Math and science share a side of problem elaboration and solving. So it would contradict Buddhism if you enjoy or think it is meaningful to be worried about all those problems. Over-thinking about anything and having a heavy attitude over theories or facts are opposite to the practice of meditation.
The point of meditation is to not being absorbed to mental elaborations. So there is no sense to think all over a sitting session. Then this extends to daily life, there is no sense to have a sharp and clear mind when meditating and daydream in the rest of the time.
For short, the point isn't what phenomena you engage, but it's how you engage to phenomena. If you can elaborate on any philosophy in a detached way it wouldn't be a problem at all. So the practice would be to think while being present and aware. (yes, this one is quite paradoxical)

I would like to point out that this is essentially a Hinayana view, and is not universally applicable to all Paths. Another view is that to be totally absorbed (completely un-distracted) by a topic of any kind is the same as concentration meditation, and has the same effect on mind. This means that enjoying doing problem solving is not contradictory to Buddhism, any more than enjoying your meal totally would be. Then, you are left with contemplative and spacious meditation to do separately.

Study of mathematics or science in and of itself is orthogonal to practice of Buddha-Dharma. But a side effect of study can often be a sense of pride based on the false conviction that one now knows everything there is to know about the way the world operates. This could be a serious barrier for entry into Buddhism and a source of misinterpretation of what Buddhism is actually about.

Mathematics, science, logic fall to the field of perception. If you conceptualize things and hold on to them as reality then this can be a hindrance.
You have to try to see things as they are without the clouding of perception.
Initially perceptions will be strong, but when perceptions arise you should try to be equanimous without clinging or reacting to the sensations associated with the perception and it's trigger. With this your perception weakens, and ultimately when you realize some form of sainthood, it ceases momentarily.

I don't agree with the spirit of your comment... everything we do or think falls to the field of perception, including the suttas, and everything else about "practicing" a path. We cannot be outside of perception as it is the only way to receive knowledge. The clouding of perception is not quite accurate either.. it is the clouding of the mind, believing that perception IS reality, that is the problem we are trying to solve. Perception cannot cloud the mind, the system of mind is prone to being clouded by WHAT we perceive as being real, which is what causes clouding.

If you are a Tantric Buddhist, you could use Mathematics and Science AS a path to enlightenment.
Also, the word 'wrong' is not relative to some 'right' which is known to Buddhists. The Eightfold path is a conjecture that "seems to work ok", but the Buddha himself said there were innumerable paths besides it.
So, this question could be answered in many ways, from many different viewpoints. It all depends on how you have decided to practice.
Buddhism is too large a viewpoint to answer this question.. you need to narrow it to what vehicle, and even flavor, of Buddhism as it is practiced in the world to get a meaningful answer.
EDIT: It seems that many here are pointing out that studying a difficult subject outside of Buddhism can lead to pride or distraction or attachment. I agree.
The broad point I am trying to make is that this is not any different than being prideful in anything, and does not in itself constitute a danger to your path, any more than being prideful in your appearance, strength, or taste in wine would be. In this way, there is no difference between Math and Literature, or between Physics and Dharma Studies. Thus, I maintain that there is no area of knowledge that will lead you to being more prone to pride, as long as you maintain your path while learning it.

I don't understand the first paragraph (which says that "a Tantric Buddhist could use Mathematics and Science as a path to enlightenment")? Could you add at least a little explanation of what Tantric Buddhism is, to clarify how it could use maths and science as a path, or to clarify what its path to enlightenment may be?

Well, the first thing is.. Enlightenment is Enlightenment. We can analogize that "one apple is very much like any other apple".
Secondly, Enlightenment comes in flavors, which are predicated by the path down which one walks. Every individual's attainment is different, and has a different flavor.
There are many different paths. The broad path called "Tantric" or "Vajrayana" is one which is interested in using all ordinary experience in the process of discovery. This includes learning Mathematics or Physics, and applying it to realization through contemplation.

The Right View of the Dhamma is only related to spiritual liberation i.e. the permanent cessation of suffering. Wrong Views are views that contradict Right View e.g. eternalism, annihilationism etc.
Science and mathematics are neither Wrong View nor Right View. They are simply worldly knowledge unrelated to spiritual liberation.
Lay people are taught to practise the Five Precepts and maintain livelihood in accordance with Right Livelihood for lay persons as taught in AN 5.177. In the sutta quote below, we see the Buddha praising the lay characteristic of being consummate in initiative, for mastering and practising worldly crafts. Lay persons need it for their livelihood.
So, science, mathematics and other worldly knowledge are not wrong view. But of course, any kind of exertion in worldly endeavors can lead one to strengthen their sensual cravings and cravings to become something.

[The Blessed One said:] "There are these four qualities, TigerPaw,
that lead to a lay person's happiness and well-being in this life.
Which four? Being consummate in initiative, being consummate in
vigilance, admirable friendship, and maintaining one's livelihood in
tune.
"And what does it mean to be consummate in initiative? There is the
case where a lay person, by whatever occupation he makes his living —
whether by farming or trading or cattle tending or archery or as a
king's man or by any other craft — is clever and untiring at it,
endowed with discrimination in its techniques, enough to arrange and
carry it out. This is called being consummate in initiative.
AN 8.54

The world is full of ideas. The ideas themselves do not cause wrong view. The solution is not ignorance. Opening one's mind to them, or education, is the opposite of ignorance. The Mind and Life Institute is a living example of doing so by one of Buddhism's most advanced practitioners -  the Dalai Lama.

To be short and to the point, no. It is my understanding that Pure Desire is the absolute teaching of Buddhism. So, as long as you don't get the feeling that you must due to the desire, you should still reach nirvana based on this issue.

Welcome to Buddhism SE. Maybe you could elaborate on the content of your post, i.e. what "Pure Desire" is and why one must not get that feeling. Thank you.

I think wrong learning is always problematic and likewise wrong convictions.
The scientific method of doing experiments for discovery & faĺsification is really a general modus of reasoning & acquisition of knowledge.
It is said that a mathematician's greatest weapon is proof by contradiction and to me he doesn't really care what it is he proves.
Mathematics to me is about putting aside one's delusion and just following wisdom.
Ie
At some point nobody knew how to count a negative multiplied by a negative and would speculate about it until someone actually set up an equation and saw the relations & the answer with intellect.
To me the Bodhisatta likewise developed wholesome lines of reasoning until these came together to paint a perfect picture of the elements & their conditional relations; he saw that 5 aggregates are not self, he saw that 4 aggregates have objects & are conjoined, he saw that the element which is called mind consciousness or intellect arises as one thing & ceases as another.
To me science isn't about views but rather truth & falsification of dumb ideas.
To me Buddhism was most impressive because i saw that the Buddha knew things which i've been told he weren't supposed to know, things that are recent scientific discovery & theory.
It is just very impressive because at that point him knowing these things is  basically a scientific miracle which a person trained in those disciplines can recognize as such.


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What is the role of karma in rebirth?
Rebirth is not reincarnation.  How then does the karma of an individual affect their rebirth?
In reincarnation, an individual's karma results in a better or worse next life for their soul. But in rebirth, there is no soul. So why should we care about our karma regarding our rebirth?

I'm not sure I understand how these two sentences are related. Can you elaborate?

In reincarnation, an individual's karma results in a better or worse next life for their soul.  But in rebirth, there is no soul.  So why should we care about our karma regarding our rebirth?

Can you update your question so people will be better equipped to answer?

Thanks for the update :) Why should we care about karma at all? We change from one moment to the next, so really we're born every moment, yet it obviously changes us from moment to moment.

@Yuttadhammo I agree but I'm still pondering anatta, karma and rebirth. :-)

In reincarnation, an individual's karma results in a better or worse
  next life for their soul. But in rebirth, there is no soul. So why
  should we care about our karma regarding our rebirth?

There is no Soul, but still there is consciousness. All suffering we are experiencing now  (in this life) is caused by past unwholesome deeds. So why cause suffering for future life? Yes, that person will not know about us, but still his consciousness will be in our stream of consciousness, related to ours, and even though we will not know why, we will suffer (or enjoy fruits of wholesome deeds).
Different argument. Basically, consciousness in our current life is as changing as between the lives. So, from this point of view, there is no difference when to suffer (or enjoy) - in the future of this or next life. If you don't want to suffer in this life why would you cause suffering in the next?

But in rebirth, there is no soul

The Buddha didn't say there was no soul.
The problem with saying there is a self or there is "no self" requires a view which the Buddha said was incompatible with the practice:

... a certain monk said to the Blessed One: "Which birth, lord? And whose is this birth?"
"Not a valid question," the Blessed One said.
  If one were to ask, 'Which birth? And whose is this birth?'
  and if one were to ask,
  'Is birth one thing, and is this the birth of someone/something else?'
  both of them would have the same meaning,
  even though their words would differ.
  When there is the view that the soul is the same as the body, there isn't the leading of the holy life.
And when there is the view that the soul is one thing and the body another, there isn't the leading of the holy life.
  Avoiding these two extremes, the Tathagata points out the Dhamma in between: From becoming as a requisite condition comes birth."
SN 12.35

He didn't say the one thing (there is a self) or the other thing (there is no self), he said the thing in the middle, which is that with certain phenomena as a requisite condition, other phenomena arise.
He didn't answer the big question of what does and does not exist, he answered the small question about how a thing arises.
Some reading: No-self or Not-self?

So why should we care about our karma regarding our rebirth

One thing that the Buddha consistently affirmed, though, is the efficacy of action and the results of kamma. He would go out of his way (MN 101) to refute ideas that personal action had no consequences or was totally predetermined.
He just didn't link together action and an individual's identity through multiple lifetimes or say that they weren't linked. Either view prevents the living of the holy life.
Seeing action as efficacious and producing results is the thing that is necessary; understanding the arising of phenomena is necessary. Talking about souls is not necessary.

As I've said elsewhere (here and here), death is just a concept. The reality is that the mental and physical aspects of experience arise and cease incessantly, and are governed by complex laws of cause and effect (i.e. karma). Since this process isn't categorically affected by conceptual death, you should be as concerned about how your karma will affect your next life as you are about how it affects this life (or unconcerned, as the case may be).
There is one proviso to that, of course; death is a profound experience that resets much of the nature of one's experience, leaving one without much familiar to cling to; it is thus a time of vulnerability, where one is more prone to cling to past karma and be reborn according often to a seemingly random mind state that just happened to pop into your head at the moment of death. Dangerous for those without mental clarity.

I'm confused. Your statement appears to imply that there is such a thing as a soul.

It's the same reason why you eat good food instead of spoilt food. Because spoilt food gives you a stomach ache. It's a simple matter of causes and effect. There's no soul involved at any place.


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Attachment is a poison. Why is attachment to the Buddha and to Buddhist philosophy not a problem?
Attachment (aka craving or greed) is one of the Three Poisons.  Why is attachment to Buddha not a poison?  Perhaps it's related to the Tibetan Buddhist lojong "Don't make gods into demons"?

Who says it's not a poison? Sounds poisonous to me :)

@yuttadhammo, you are monk, yes?  How are you not attached to the Buddha?

Why does being a monk necessitate attachment to the Buddha?

@yuttadhamo, I asked first. ;-)

My question is better :P

One Zen master stopped using the word "Buddha" because people overused the word so. He [taught] "From now on, every time I use the word 'Buddha,' I will go to the river and wash my mouth out three times." His statement is completely in accord with the dialectics of prajnaparamita, but when people heard his words, they thought he was being disrespectful. Only one [person]  understood. He stood up and said, ["I appreciate your words. Every time I hear you say the word 'Buddha,' I will go to the river and wash out my ears three times."] - Thich Nhat Hahn - The Diamond That Cuts Through Illusion

Possible duplicate of Isnt the desire for giving up the desires, a desire?

Sez who?
Attachment to Buddhism and to Buddhist philosophy is a very serious problem, which every practitioner should be careful about, since it's so seductive: it's easy to be perceived as progress, whereas it's the very opposite of progress.
To counter this hazard, some Zen schools recommend that "if you come across the Buddha on the road, kill him!" (Not to be taken too literally.)

Buddhism is a "kayak" (a guide) that takes one from the endless sea of sufferings to find a harbor. What would one do in order to commence and land on the harbor?
Leave the kayak - Buddhism - and disembark.
If not, one is attached to the kayak. Still at sea.
The sea of sufferings.

My understanding is that the Buddha taught that we should not attach ourselves to him or his teachings.  If we find that his teachings don't work, then we should feel free to leave them behind and pursue other paths.
That said, there is also the idea that some attachments are better than others.  For example it is probably better for an alcoholic to replace their attachment to alcohol with an attachment to the 12 steps of Alcoholics Anonymous.  Likewise, it would be better for someone who is attached to suffering or causing suffering in others to replace that with an attachment to the Buddha's teachings.

Good answer.  The umbilical cord always has to be cut sooner or later, but definitely better to be attached to eating food than eating, say, rocks.

If someone is insulting the Buddha and the Dhamma, and you become hurt, you are poisoned!  But if you feel neutral (Uppekha) or compassionate (Karuna) towards the person, you are fine!

Do the teachings of the Buddha cause you suffering? If not, perhaps it's ok to hang on to them for a little while longer on this journey. :)
I find Buddhism refreshing in this manner as the teachings of some other religions actually do cause suffering for their followers. For example people who are excluded from participating fully in their chosen houses of worship due to sexual orientation.

Identifying with something doesn't necessarily mean you're attached to it, especially if that something is just your way of living. I identify best with Zen Buddhism, but I'm not attached to it any more than I'm attached to my own consciousness; it's just become how I think, which dictates how I feel.
Attachments are bad because if you lose them, you suffer.  I can't 'lose' Zen without completely losing myself, which is going to happen to all of us one day or another :) Preference is also commonly confused with attachment. I prefer a certain knife in my kitchen drawer for slicing tomatoes, but I wouldn't be at all upset if it wasn't there one day, I'd simply replace it.
A part of daily meditation can be imagining losing that which you value the most, so you've experienced it when it ultimately happens, which softens or even mitigates the suffering that might otherwise ensue. If you can't do that with something, then it's probably not something you could become attached to, but more just a part of your being.

Actually Buddha stated in his suttas after following the Eight Fold Path to attain Nibbana, you should give up the path when you attain the supreme bliss of Nibbana. It is something like this; think that you wanna cross a river. There's no boat near by. So you collect wood and creepers and finally build a small boat and you cross the river using it. After crossing the river, will you carry the boat with you where ever you go thinking "this boat helped me to cross the river"? No. You'll leave the boat by the river and you'll go where you need to go. Buddha state that similarly one should give up the eight fold path after perfectly attaining the supreme bliss of Nibbana.

@THelper to elaborate on Toby's point. To call oneself a buddhist is to identify oneself with an ideological construct and therefore to dwell in a mental fabrication. The ideas of buddhism are arranged into a belief system more commonly known as a view. To associate your self with this view, is exactly the kind of housebuilding which the buddha espoused against in practically every sutra. Buddhism is the only "religion" which fervently encourages its followers to abandon any part of the belief system when it begins to hold them back rather than help them.

You should have confidence and gratitude towards the Buddha. If this becomes a strong attachment this will hinder your progress on the path. The story of Vakkali is a good example.
If you are dealing with Buddhism as a phylosophy then you are dealing with matters at a conceptual level. This is feeding into your perception than helping towards the cessation of perception.

If one calls oneself a Buddhist, one has already missed the point.
---  from a teacher my daughter had.

Welcome to Buddhism SE! Could you please elaborate on this? We prefer all answers here to be self-explaining. I think I understand what you mean, but I'm not sure all future readers will also.

@THelper This answer elaborates on Toby's point.

I think there is a misunderstanding here. Buddha was not a Buddhist, he was not attached to the previous Buddha (Kassapa) and still the attained the maxium goal. Becoming a Buddha or an Arahant does not require attachment, on the contrary, it requires deattachment and equanimity.
Don't think about Buddhism as a tradicional religion, it is more like an analysis of the laws of the universe (both inside and outside), Buddha was simply explaining how things work, what the mind is, the best path to take and the consequences of good and bad deeds.

Why is attachment to Buddha not a poison?
Because Buddhism (attachment to Buddha, Sangha, Dharma) has meta-attachment:
it teaches to even let go of Buddhism itself--but only once one has mastered Buddhism's practices and not a moment sooner. To be detached from Buddhism a moment sooner would be like a HS student dropping out before he finished.
In short: Buddhism teaches detachment from Buddhism itself.
No other tradition does this.


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Is drinking coffee or tea against the fifth precept?
The fifth precept most directly guides us to abstain from alcohol. Coffee is a stimulant and probably so is tea. Drinking either beverage affects our mental calm and makes us behave in ways that we would not do so without having drunk it. In this sense, drinking coffee and tea is not that different from drinking alcohol. Does drinking coffee or tea is considered against the fifth precept?
In Asia, many people, including monks, drink tea. Does this indicate that drinking tea is at least not against the fifth precept?

The literal meaing there is avoiding fermented drink that causes heedlessness.

Surā-meraya-majja-pamāda-ṭṭhānā veramaṇī sikkhāpadaṃ samādiyāmi
I undertake the precept to avoid [that big long word]

Big long word happily rendered as "beer-cider-carelessness-intoxication-condition" by Kare.
This is talking specifically about fermented things like beer, wine, etc. Neither coffee nor tea are fermented, nor do they cause heedlessness. I've heard of monks drinking tea. (I've heard of monks smoking too, which I think isn't forbidden by this rule, although perhaps by others)
It's all well and good to look past the behavior prohibited by the precepts to see what further kinds of attachments you have that can be abandoned, but not, I think, at the cost of going back to change the meaning of the precept.
But I do occasionally see attempts at redefining the precepts to be stricter than they are. Take Sulak Sivaraksa's reinterpretation of the five precepts:

Sulak reinterprets the five classic Buddhist precepts for the modern day.

Individuals may not be killing outright, but they must examine how their actions might support wars, racial conflict, or the breeding of animals for human consumption.
Considering the second precept of abstaining from stealing, Sulak questions the moral implications of capitalism.
Stopping exploitation of women is a natural extension of the third precept of abstaining from sexual misconduct.
And vowing to abstain from false speech would naturally bring into question how mass media and education promote a biased view of the world.
Finally, the fifth precept to avoid intoxicants deals with international peace and justice because, “the Third World farmers grow heroin, coca, coffee, and tobacco because the economic system makes it impossible for them to support themselves growing rice and vegetables.

All good points and things worth thinking about, but these are going beyond the five precepts. The precepts are intended to take you to a point where you can examine all of your behavior to see what is skillful, what leads to affliction, etc.
But the precepts shouldn't be redefined to also include these new things. This would only lead to divisiveness between people as one person preaches getting rid of coffee and others disagree. Remember the Buddha refused to make vegetarianism mandatory for the sangha, even though the killing involved in eating meat can easily be seen to pertain to the first precept.
In the case of coffee, I could see a person getting riled up by it and possibly being less able to control their mind, being quicker to anger, etc. If this is the case, then it should certainly be examined, and perhaps that behavior should be abandoned, but this is not covered by the fifth precept.

When I drink coffee, I am more talkative than usual. In this sense, the simulation caused by coffee can be considered heedless, although coffee is not fermented drink.

This is a very small factual note that doesn't inform the material meaning of your post, but it is worth noting that there are many kinds of tea that are fermented - but they are fermented as a part of an aging and storage process, not as a means of forming an alcohol. See: https://en.wikipedia.org/wiki/Fermented_tea

The five precepts are an entry-level practice that is designed to help practitioner master basic discipline of self-reflection and self-control.
Abstaining from killing, stealing etc. implies basic ability to watch one's mind for harmful thoughts and emotions, and to prevent them from getting acted out.
In light of the above, the no-killing rule should not be understood literally, as an absolute law, but as a guideline for training the mind. It is not acceptable to hurt or harm any creature (big or small) out of antipathy. This is what the no-killing rule is mostly about, countering the first poison, usually translated Anger or Hate but really meaning Aversion/Antipathy/Negativity.
Similarly, the no-stealing rule is mainly about countering another of Three Poisons, that of Obsessive Attraction or Desire.
Likewise, the no-intoxication rule is meant to counter the habitual mind-state of Ignorance (obscurity, confusion). Many people prefer to get drunk or stoned as a way to anesthetize themselves. They don't seem to see the connection between the dimmed mind and the causes of suffering. The no-intoxication rule is meant to guide people out of their comfortable haze and towards lucidity of enlightenment. In this vein, watching TV or playing videogames, is too a form of intoxication and should be minimized.
Drinking tea or coffee does not produce haze and therefore is not subject to the fifth precept. That said, being addicted to e.g. coffee is not much different from any other addiction in that produces a state of obsessive desire.

Very good explanation of how things are linked up. This is what is really needed when learning.

A more literal interpretation is, for example, from Bhikkhu Bodhi

"The fifth precept reads: Suramerayamajjapamadatthana veramani sikkhapadam samadiyami, "I undertake the training rule to abstain from fermented and distilled intoxicants which are the basis for heedlessness."

Coffee & tea, not being fermented or distilled intoxicants wouldn't break the 5th precept I wouldn't think. Of course limiting caffeine and sugar and lots of other stuff will help keep your mind calm and makes sense for good health and meditation.

I think that the Heedlessness idea is on track. The Buddha didn't warn against cocaine, heroin or methamphetamine, but they can clearly be included in the 5th Precept these days. I think the issue would be how do coffee and tea affect you? You might abstain to see. You might have them for a reason. I don't hold absolutely with the "addiction" line because we are all addicted to sunlight, air, water and food. More or less of any of them might help or harm. Coffee and tea are no more inherently harmful than any of these. The fact that 90% of the worlds people use caffeine on a daily basis should tell us something. (What should it tell us?)
Black tea is fermented, by the way. Green tea is not.

Tea or coffee drinking is not an issue. This is well explained in "THE FIVE PRECEPTS" which is a very good read on the 5 precepts.

The fifth precept reads: Surā-meraya-majja-pamāda-ṭṭhānā veramaṇī sikkhāpadaṃ samādiyāmi, “I undertake the training rule to abstain from fermented and distilled intoxicants which are the basis for heedlessness.” The word meraya means fermented liquors, sura liquors which have been distilled to increase their strength and flavor. The world majja, meaning an intoxicant, can be related to the rest of the passage either as qualified by sura,meraya or as additional to them. In the former case the whole phrase means fermented and distilled liquors which are intoxicants, in the latter it means fermented and distilled liquors and other intoxicants. If this second reading is adopted the precept would explicitly include intoxicating drugs used non-medicinally, such as the opiates, hemp, and psychedelics. But even on the first reading the precept implicitly proscribes these drugs by way of its guiding purpose, which is to prevent heedlessness caused by the taking of intoxicating substances.

The wording of this source is indeed very clear, concise and pleasant to read. Thank you.

Why do you think that psychedelics cause heedlessness?

@Euphorbium perhaps a larger concern is that non-medical drugs alter one's experience, which goes against the entire point of practicing Buddhism.


text:
Buddhism and bacteria
Buddhist teachings tell that all intentional killing is negative karma. So, what about bacteria? Are bacteria considered to be sentient beings? Is using antibiotics negative karma?
Is it possible to reborn as a bacterium?

Bacteria are not understood to be sentient (Wikipedia: Sentience is the ability to feel, perceive, or to experience subjectivity), so probably not. However, perhaps the intention of killing could have negative karmic effects. As opposed to cure an organism (i.e. human) or clean something to avoid contagion.

@yuttadhammo has replied to the same question at http://ask.sirimangalo.org/1560/bacterial-rebirth-and-karma - see Q4.

Not a complete duplicate, but related to killing http://buddhism.stackexchange.com/questions/87/is-killing-vermin-and-insects-justifiable

As I pointed out in my answer to "are earthworms our mothers?"  these kind of questions often assume incorrect frame of reference, different from the one Buddhism operates in. The point of teachings is to produce a certain state of mind, that will affect your behavior in certain way, that will eventually lead to better results, up to and including Enlightenment for you and the rest of the sentient beings.
The Five Precepts (no killing, stealing, speaking nonfactually, letting sensual pleasure control you, getting intoxicated) are an entry-level practice that is designed to help practitioner master basic discipline of self-reflection and self-control. Abstaining from killing, stealing etc. implies basic ability to watch one's mind for harmful thoughts and emotions, and to prevent them from getting acted out.
In light of the above, the no-killing rule should not be understood literally, as an absolute law, but as a guideline for training the mind. It is not acceptable to hurt or harm any creature (big or small) out of antipathy, obsessive desire, or ignorance. This is what Five Precepts are mostly about, countering the Three Poisons.
For reference, the Three Poisons are three basic moods afflicting the mind, impairing one's judgement and goal-making abilities:

Anger/Hate/Irritation/Aversion/Antipathy/Negativity
Lust/Desire/Attraction/Obsession
Ignorance/Confusion/Sloth/Torpor

Most people use antibiotics out of desire to cure illness, or out of aversion towards the illness, so your answer seems to imply that using antibiotics to cure illness does produce bad kamma. Do I understand it correctly?

No, you do not!

Is it because the aversion is towards the illness, and not towards bacteria? Or for some other reason? I think the answer is a bit unclear.


text:
Vajrayana Buddhism relies on a teacher-pupil relationship. What in tradition or the literature explains how to find the appropriate teacher?

Vajrayana Buddhism is esoteric, in the sense that the transmission of certain teachings only occurs directly from teacher to student during an initiation or empowerment and cannot be simply learned from a book. Many techniques are also commonly said to be secret, but some Vajrayana teachers have responded that secrecy itself is not important and only a side-effect of the reality that the techniques have no validity outside the teacher-student lineage.
  (Source: http://en.wikipedia.org/wiki/Vajrayana#Esoteric_transmission)

But in my travels through the Buddhist landscape, I find that teachers are human: some good, some mediocre.  How do I find the right teacher?  Are there tests that the student can apply to the teacher?

"The Words of My Perfect Teacher" by Patrul Rinpoche has a chapter (Ch. 6) on how to choose, test and follow a "spiritual friend" (teacher):

pure, never having contravened any of the commitments or prohibitions (Pratimoksha, Bodhisattva's Vow, Secret Vows of Secret Mantrayana)
unstained by negative emotions
learned, not lacking in knowledge of sutras, tantras and shastras
heart suffused with compassion, loves each being like his only child
well-versed in vast array of rituals and ceremonies
not merely verbal but by putting the meaning of teaching into practice has actualized in himself the achievements of riddance and realization
generous, completely free of attachments
language should be pleasant
teaches each according to person's needs
acts in accordance with what he teaches

Teachers to avoid:

Like a millstone made of wool (high lamas by birth but have not studied and practiced seriously enough for the above qualities to arise)
Like the frog that lived in a well (with very limited exposure to true depth and breadth of Practice, having never seen a genuine spiritual master)
Mad guides (loose in discipline, strong in emotions, overemphasizing the esoteric and transcendental)
Blind guides (don't know what they are talking about)

"Treasury of Precious Qualities" by Jigme Lingpa has several pages (in Ch.5) on fully qualified masters vs. false teachers:
(repeats most of the above and adds the following)

Good teacher must have few activities, exclusively preoccupied with Dharma
His presence has transforming effect, inspiring all who meet him to seek for liberation
Must have an unconfined view, having realized the equality of nirvana and samsara
Having direct experience of the above, he is the source of his own freedom
Has been ripened by empowerments that came down to him in an uninterrupted lineage.

Could you quote some of this, if it's not too much trouble?

@KevinJohnsrude, added

Here is one more link to some good commentary on finding a good teacher from one of my favorite teaches, Alex Berzin: "Relating to a Spiritual Teacher: Building a Healthy Relationship",  http://www.berzinarchives.com/web/x/nav/group.html_1305527811.html

The "Jewel Ornament of Liberation" by Gampopa describes different levels of teachers and their qualifications. Some rely on the 31st chapter of the Avatamsaka Sutra (also known independently as the "Sutra of the Ten Bhumis") which describes a set of criteria on which to judge someone as a Mahayana teacher.
edit: it occurs to me that you may have been wondering about specifics, not just where you can find it talked about.
Some basics would be: have they taken the Bodhisattva Vow? Do they have demonstrable knowledge of the Mahayana path? Are they patient while teaching? Do they make sure people understand? Do they seem to get discouraged or disappointed with students? Can they speak to you at your level of understanding?
And of course standard things like ethical behavior.

What is the Bodhisattva Vow?

The Bodhisattva Vow is a life-transcending vow to attain full-Buddhahood to benefit all sentient beings. If you took the vow in this life, that vow would continue into future lives as well. The mindstream would be "stained" by it creating tendencies towards the dharma and repeating the vow in those future lives (in theory).

(Disclaimer: This is not a Vajrayāna approach so feel free to discard it but I'd say the advice is useful nonetheless.)
To find a skillful teacher, one could approach the matter prudently by trying to get the most points checked from the following list:

Doesn't accept any money, especially for teaching.1
Has the qualities mentioned in AN 4.73 & AN 4.192.
Doesn't show traces of greed, hatred or delusion in their behavior.
Meditates frequently and for lengthy periods.
Eats once a day before noon.2
Is content with very little.3
Is bent on solitude & seclusion.4

Note that these points are just good guidelines and should be taken as a supplement to one's own discernment.
For further references, you might want to read some early discourses concerning this:

DN 12: Teachers that are worthy & unworthy of criticism.
MN 8: The whole discourse is worth reading but I linked to the specific section about instruction called "Quenching".
MN 47: This discourse addresses the issue head-on.
AN 5.100: Teachers being covered up by their pupils.
AN 5.159: Five qualities a teacher should set up.
Dhp 158-159: Two verses about teachers.

Footnotes:

AN 5.159 has five qualities a teacher should set up. The fourth one is that he will not speak for the purpose of material reward.
MN 65 is a good reference about the Buddha's thoughts concerning this issue.
AN 4.27 is a good reminder about contentment with the bare minimum but I wouldn't advocate it as a necessary guideline.
AN 8.53 has the qualities that make-up the Buddha's teaching and one of them is solitude\seclusion.

I would have voted you the answer but your answer needed more text and fewer references.

When it is possible, I prefer to let the texts speak for themselves. Additionally, the question mentions "What in tradition or the literature explains how to find the appropriate teacher?", so the answer seems quite to the point apart from not being Vajrayāna as already mentioned in the disclaimer. Thank you for the comment anyway.

I disagree with the comment "Don't accept money, especially for a teaching."
I am not sure where that particular comment comes from, but as both a Tibetan practitioner and an ordained monk, I have  Never seen it written that one should not accept a teacher who is paid for his/her teachings. In fact, and supporting teachers, who traveled from afar, individuals, benefactors, and Dharma centers all make donations to the teacher.
Most likely, the implication is that students should be wary of teachers who appear to be"money – hungry."
Finally, if you find yourself in a group where money and making money seem to be more important than teachings and/or Dharma, it is probably not a good place to be.

Did you see the "Disclaimer: This is not a Vajrayāna approach" at the top of that message? It references the Udayi Sutta which says, "The Dhamma should be taught with the thought, 'I will speak not for the purpose of material reward.'"


text:
What does Buddhism literature and tradition say about transgender folks?
This may seem like a question that is far too modern for an ancient tradition, but when I traveled in Thailand I learned that katoeys (male-to-female) are a legal gender in Thailand.  What does Buddhism say about the folks who experience discomfort or distress because there is a mismatch between their biological sex and gender identity?
As it becomes less dangerous for transgender folks to change, I am finding out that several of my friends are transgender and I would like to know what Buddhism offers them.

Answers to this question should be careful to avoid being anachronistic - modern conceptions of transgender identity (even in places where it's better-established, like Thailand [kathoeys] or India [hijras]) are much younger than Buddhism, and as such, the texts could only possibly have referred to other (albeit possibly related) conceptions of fluid or indeterminate gender.

This link may be helpful. Transgendered People And Buddhism by Shravasti Dhammika:

The Tipitaka mentions several different types of transgendered states and individuals – the man-like woman (vepurisika), sexual indistinctness (sambhinna), one having the characteristics of both genders (ubhatovyanjanaka), etc (Vin.III,129). The interesting thing is that such states and individuals are taken for granted in the scriptures with little or no moral judgments being attached to them.

There is also the International Transgender Buddhist Sangha
Here is a quote from the International Transgender Buddhist Sangha
 blog:

"The Vinaya Pitaka, the ancient Buddhist texts that define the rules for Buddhist monks and nuns, record two incidences of sex change that a monk and a nun had gone through. A group of monks and nuns bring the two incidences to the Buddha’s notice. The Buddha accepts their changed status. He allows the former male disciple who became a female to live with female disciples, and the former female disciple to live with males.
These episodes indicate the Buddha’s open-mindedness toward transsexual persons. He accepted their bodily changes even though some in his society attributed such changes to the influence of bad Karmas. [...]  There is every reason to believe that the Buddha accepted all kinds of people irrespective of any differences they had undergone.

Facebook group of the International Transgender Buddhist Sangha

It would be helpful to give a small description of what is in the links you share. Looking at your answer it is hard to tell what is your general input to the discussion. Thank you.

understandable, although I had assumed the name of the link matching the question was obvious enough to not have to extrapolate.
perhaps quoting a paragraph from the link might work.

Links only answers are discouraged on all SE sites. This is because the answer becomes worthless if the links go dead. It's best to summarize the relevant main points of each linked site in your own words and provide the link merely as background.

I updated the original to include a quote from the  International Transgender Buddhist Sangha blog link. Will read the sdhammika blog article too and pull out a quote or two from it.

Submitted another response edit to include a quote from the Shravasti Dhammika blog article that refers to various terms from the tipataka and makes reference to the source, though I didn't check the sources yet. The article also has a theory about rebirth causing "transgenderism" but no sources and really it's just speculation. It ends with a supportive message supposing that a genuine application of the dhamma would mean supporting trans people socially.

The Bodhisattva Avalokitesvara can be seen as having an indeterminate gender. Quoting from this website

One interpretation of this development contends that the bodhisattva
  is neither male or female but has transcended sexual distinctions
  [...] the flowing drapery and soft contours of the body seen in
  statues and paintings have been intentionally combined with a visible
  moustache to emphasize the absence of sexual identity.

So the issue of gender can take on a more flexible interpretation with some more Mahayana aspects of Buddhism

The Theravada tradition doesn't condemn such people. The essence of Theravadin morality is expressed in the Ambalatthika-Rahulovada Sutta like so:

"What do you think, Rahula: What is a mirror for?"
"For reflection, sir."
"In the same way, Rahula, bodily actions, verbal actions, & mental
  actions are to be done with repeated reflection.
"Whenever you want to do a bodily action, you should reflect on it:
  'This bodily action I want to do — would it lead to self-affliction,
  to the affliction of others, or to both? Would it be an unskillful
  bodily action, with painful consequences, painful results?' If, on
  reflection, you know that it would lead to self-affliction, to the
  affliction of others, or to both; it would be an unskillful bodily
  action with painful consequences, painful results, then any bodily
  action of that sort is absolutely unfit for you to do. But if on
  reflection you know that it would not cause affliction... it would be
  a skillful bodily action with pleasant consequences, pleasant results,
  then any bodily action of that sort is fit for you to do.
"While you are doing a bodily action, you should reflect on it: 'This
  bodily action I am doing — is it leading to self-affliction, to the
  affliction of others, or to both? Is it an unskillful bodily action,
  with painful consequences, painful results?' If, on reflection, you
  know that it is leading to self-affliction, to the affliction of
  others, or to both... you should give it up. But if on reflection you
  know that it is not... you may continue with it.
"Having done a bodily action, you should reflect on it: 'This bodily
  action I have done — did it lead to self-affliction, to the affliction
  of others, or to both? Was it an unskillful bodily action, with
  painful consequences, painful results?' If, on reflection, you know
  that it led to self-affliction, to the affliction of others, or to
  both; it was an unskillful bodily action with painful consequences,
  painful results, then you should confess it, reveal it, lay it open to
  the Teacher or to a knowledgeable companion in the holy life. Having
  confessed it... you should exercise restraint in the future. But if on
  reflection you know that it did not lead to affliction... it was a
  skillful bodily action with pleasant consequences, pleasant results,
  then you should stay mentally refreshed & joyful, training day & night
  in skillful mental qualities.
"Whenever you want to do a verbal action, you should reflect on it:
  'This verbal action I want to do — would it lead to self-affliction,
  to the affliction of others, or to both? Would it be an unskillful
  verbal action, with painful consequences, painful results?' If, on
  reflection, you know that it would lead to self-affliction, to the
  affliction of others, or to both; it would be an unskillful verbal
  action with painful consequences, painful results, then any verbal
  action of that sort is absolutely unfit for you to do. But if on
  reflection you know that it would not cause affliction... it would be
  a skillful verbal action with pleasant consequences, pleasant results,
  then any verbal action of that sort is fit for you to do.
"While you are doing a verbal action, you should reflect on it: 'This
  verbal action I am doing — is it leading to self-affliction, to the
  affliction of others, or to both? Is it an unskillful verbal action,
  with painful consequences, painful results?' If, on reflection, you
  know that it is leading to self-affliction, to the affliction of
  others, or to both... you should give it up. But if on reflection you
  know that it is not... you may continue with it.
"Having done a verbal action, you should reflect on it: 'This verbal
  action I have done — did it lead to self-affliction, to the affliction
  of others, or to both? Was it an unskillful verbal action, with
  painful consequences, painful results?' If, on reflection, you know
  that it led to self-affliction, to the affliction of others, or to
  both; it was an unskillful verbal action with painful consequences,
  painful results, then you should confess it, reveal it, lay it open to
  the Teacher or to a knowledgeable companion in the holy life. Having
  confessed it... you should exercise restraint in the future. But if on
  reflection you know that it did not lead to affliction... it was a
  skillful verbal action with pleasant consequences, pleasant results,
  then you should stay mentally refreshed & joyful, training day & night
  in skillful mental qualities.
"Whenever you want to do a mental action, you should reflect on it:
  'This mental action I want to do — would it lead to self-affliction,
  to the affliction of others, or to both? Would it be an unskillful
  mental action, with painful consequences, painful results?' If, on
  reflection, you know that it would lead to self-affliction, to the
  affliction of others, or to both; it would be an unskillful mental
  action with painful consequences, painful results, then any mental
  action of that sort is absolutely unfit for you to do. But if on
  reflection you know that it would not cause affliction... it would be
  a skillful mental action with pleasant consequences, pleasant results,
  then any mental action of that sort is fit for you to do.
"While you are doing a mental action, you should reflect on it: 'This
  mental action I am doing — is it leading to self-affliction, to the
  affliction of others, or to both? Is it an unskillful mental action,
  with painful consequences, painful results?' If, on reflection, you
  know that it is leading to self-affliction, to the affliction of
  others, or to both... you should give it up. But if on reflection you
  know that it is not... you may continue with it.
"Having done a mental action, you should reflect on it: 'This mental
  action I have done — did it lead to self-affliction, to the affliction
  of others, or to both? Was it an unskillful mental action, with
  painful consequences, painful results?' If, on reflection, you know
  that it led to self-affliction, to the affliction of others, or to
  both; it was an unskillful mental action with painful consequences,
  painful results, then you should feel distressed, ashamed, & disgusted
  with it. Feeling distressed, ashamed, & disgusted with it, you should
  exercise restraint in the future. But if on reflection you know that
  it did not lead to affliction... it was a skillful mental action with
  pleasant consequences, pleasant results, then you should stay mentally
  refreshed & joyful, training day & night in skillful mental qualities.
http://www.accesstoinsight.org/tipitaka/mn/mn.061.than.html

If something does not cause harm to one's self or to others, then from a Theravadin perspective it is morally acceptable. In my opinion the teachings of the Buddha offer many sexual minorities (such as lesbians, gays, bisexuals, and transgendered people) the clear moral teachings that affirms that they are not to be condemned.
Sexuality in general is technically classified as being unwholesome or unskillful, but the Theravada school makes a distinction between acts that are unwholesome (anything based on attachment at all, so this also includes enjoying entertainment, food, etc...) and acts that are evil. Sexuality that is within the third precept (not using sex in ways that breaks up relationships or sexual taking advantage of people etc...) is understood as being acceptable for a layperson. Although this Sutta talks about abandoning all unwholesome states of mind, it was aimed at the Ven. Rahula who was a novice monk at the time. For laypeople one only must abandon evil actions.

The institutions are all over the place. There are rules that say hermaphrodites (or probably more generally, anyone who doesn't fall into a tidy male/female gender) isn't allowed to ordain.
Then a few hundred years later you get Mahayanaists who specifically say hermaphrodites (& I supposed anyone who doesn't fall into a tidy category) are allowed to become Bodhisattva's, too. Except in Chinese Buddhism, they were still expected to give up any interest in sex.
In one of the Mahayana sutras a celestial Buddha or Bodhisattva transforms Ananda into a woman to make a point about appearances being superficial & differences being artificial. I can't find the source, if I find it I'll come back and add the ref.
And finally, in the old and new traditions, a good Buddhist woman would hope to be reborn as a man, or I suppose a man would fear doing wrong lest he be reborn as a women. This was obvious sexism, but amazing meant people were sexist, but somehow comfortable with the idea of cross-life transsexualism. It sounds progressive, but it is a odd situation where a sexist line of reasoning leads to a progressive conclusion.

In Vimalakirti sutra the goddess transforms Shariputra's to a female body.

Peter Harvey, a Buddhist scholar who focuses fairly heavily on morality in Buddhism, writes at length on "culture war" issues like this, homosexuality, abortion, etc. in the context of the Pali canon. His Introduction to Buddhist Ethics explored issues related to transgendered people, in the chapter "Homosexuality and other forms of 'queerness'.  It's worth a look.  The full text can be found here - http://www.e-reading.me/bookreader.php/142060/An_Introduction_to_Buddhist_Ethics.pdf/ and it's a good read in general.
Here is an extract:

SEX-CHANGE
Early Buddhist texts refer to the sex of a person as something that can
change within one life, as well as between lives. In the Vinaya, there is reference to a monk in whom the sexual characteristics of a woman
appeared, and a nun in whom the sexual characteristics of a man
appeared. In both cases, the Buddha appears to accept this and simply
say that the ex-monk nun should follow the rules of the nuns, and the ex-nun monk should follow the rules of the monks. In commentarial literature, the sex of a person is seen as determined at conception, but as subject
to possible change. Causes of sex-change are seen as karmic in
nature. The Dhammapada commentary tells of a man instantly turning into
a woman when he is sexually attracted to a monk; after marrying and
giving birth, she then turns back to a man when she asks the monk’s forgiveness, and goes on to become an Arahat. Sex-change, then, is not seen as limiting spiritual potential.

The word "transgender" appears once, on page 432 of the document (i.e. page 454 of the PDF file).

True, but in the chapter I mentioned Harvey treats the subject of "sex change" and gives quite a few relevant examples from sources ranging from the Vinaya, Sutta Pitaka, and commentaries.  Some of those examples do seem right on point for this question.

The stories of the "suddenly another sex" monastics do seem like a tiny part of the answer to this question, though we should definitely take them in context as being impossible to compare directly with modern trans people. Fundamentally the stories seem magical/mythological, and thus not very relevant. Maybe though the real story is "trans man (man with a vagina) found among monks" with the conclusion "that is in fact a woman, put her with nuns". If true, this story implies the answer is: At the time they forced trans people back to their birth-assigned genders.

Simple answer mind has not gender. Mind might reach enlightenment in any manifestation. Body is just temporary manifestation of mind.

This is interesting, but doesn't give us much insight into how transgender people should approach buddhism and/or how they will be treated by buddhists. It could both imply that buddhism is fine with trans people, because gender is not absolute, and that buddhism is dismissive of trans people, because trans people themselves are too absolute about their own gender.

Buddhism is firmly in support of LGBT (and transgender specifically), because shedding of boxed reified identities is shedding of conflict and suffering.

Literature and Tradition are very different. Vastly different. Binary opposites even? In judaism we have the written torah and we have the oral torah. Anything written can be classified as literature. Oral traditions exist as much as literature. But how can you find it? You cant! But you can heart it. Is this not the same of PureDhamma?