Kōan

A kōan is a story, dialogue, question, or statement in the history and lore of Chán (Zen) Buddhism, generally containing aspects that are inaccessible to rational understanding, yet may be accessible to intuition.

A famous kōan is: "Two hands clap and there is a sound; what is the sound of one hand?"

Kōans originate in the sayings and doings of sages and legendary figures, usually those authorized to teach in a lineage that regards Bodhidharma (c. 5th-6th century) as its ancestor. Kōans are said to reflect the enlightened or awakened state of such persons, and sometimes said to confound the habit of discursive thought or shock the mind into awareness. Zen teachers often recite and comment on kōans, and some Zen practitioners concentrate on kōans during meditation. Teachers may probe such students about their kōan practice using "checking questions" to validate an experience of insight (kensho) or awakening. Responses by students have included actions or gestures, "capping phrases" (jakugo), and verses inspired by the kōan.

As used by teachers, monks, and students in training, kōan can refer to a story selected from sutras and historical records, a perplexing element of the story, a concise but critical word or phrase extracted from the story, or to the story appended by poetry and commentary authored by later Zen teachers, sometimes layering commentary upon commentary.

English-speaking non-Zen practitioners sometimes use kōan to refer to an unanswerable question or a meaningless statement. However, in Zen practice, a kōan is not meaningless, and teachers often do expect students to present an appropriate response when asked about a kōan.

Even so, a kōan is not a riddle or a puzzle.
Appropriate responses to a kōan may vary according to circumstances; different teachers may demand different responses to a given kōan, and a fixed answer cannot be correct in every circumstance.

One of the most common recorded comments by a teacher on a disciple's answer is: "Even though that is true, if you do not know it yourself it does you no good."

The master is looking not for an answer in a specific form, but for evidence that the disciple has actually grasped the state of mind expressed by the kōan itself.

Thus, though there may be so-called "traditional answers" (kenjo) to many kōans, these are only preserved as exemplary answers given in the past by various masters during their own training. In reality, any answer could be correct, provided that it conveys proof of personal realization.

Kōan training can only be done with a qualified teacher who has the "eye" to see a disciple's depth of attainment.

A kōan or part of a kōan may serve as a point of concentration during meditation and other activities, often called "kōan practice" (as distinct from "kōan study", the study of kōan literature).

The purpose of kōans is for a Zen practitioner to become aware of the difference between themselves, their mind, and their beliefs that influence how they see the world as an aspect of realizing their True nature. Paradoxes tend to arouse the mind for an extended duration as the mind goes around and around trying to resolve the paradox or kōan to an "answer". This is a lot like a dog chasing its tail and, while it's chasing, the mind makes itself more visible. Once a Zen practitioner becomes aware of their mind as an independent form, the kōan makes sense and the teaching point is realized.

Zen teachers and practitioners insist that the meaning of a kōan can only be demonstrated in a live experience (after all, only you can witness your own mind and realize its nature).

Teachers have long alerted students to the danger of confusing the interpretation of a kōan with the realization of a kōan. When teachers say "do not confuse the pointing finger with the moon", they indicate that awakening is the realization of your True nature — not ability to interpret a kōan with the mind.

No amount of interpretation seems to be able to exhaust a kōan, so it's unlikely that there can be a "definitive" interpretation. Teachers typically warn against over-intellectualizing kōans, but the mysteries of kōans compel some students to place them in their original context — for example, by clarifying metaphors that were likely well-known to monks at the time the kōans originally circulated.

Other traditional kōans

Killing the Buddha
If you meet the Buddha, kill him.
— Linji

If you are thinking about Buddha, this is thinking and delusion, not awakening. One must destroy preconceptions of the Buddha.

"Kill the Buddha if the Buddha exists somewhere else. Kill the Buddha, because you should resume your own Buddha nature."

The sound of one hand
Two hands clap and there is a sound. What is the sound of one hand?
— Hakuin Ekaku
"...in the beginning a monk first thinks a kōan is an inert object upon which to focus attention; after a long period of consecutive repetition, one realizes that the kōan is also a dynamic activity, the very activity of seeking an answer to the kōan. The kōan is both the object being sought and the relentless seeking itself.
In a kōan, the self sees the self not directly but under the guise of the kōan...When one realizes ("makes real") this identity, then two hands have become one.
The practitioner becomes the kōan that he or she is trying to understand. That is the sound of one hand."

Humorous parodies of famous kōans such as:

“‘Does a dog have Buddha nature or not?’ ‘Woof’”.

“If you have ice cream I will give you some. If you have no ice cream I will take it away from you.”

(all excerpts out here have been edited from wikipedia)