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|The dreams of man|
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“”If you could in any way demonstrate or measure the Qi they're claiming to direct, you'd win the Nobel prize for physics. But why would you want that Stockholm piece of crap when you could move strangers' furniture at random, for money?
|—Penn Jillette, Penn & Teller: Bullshit!|
Qi or Chi (氣 pronounced in Standard Chinese as /tɕʰi˥˩/, in English approximated as /ˈtʃiː/) is an eastern conceptualization similar to the western idea of vitalism. Qi was based on a dualistic concept: the so-called pre-birth and post-birth qi. The Chinese believed that individuals were born with a quantity of pre-birth qi (determined by your parents and other factors) that was unreplenishable. When an individual used all of their pre-birth qi up, they died. Post-birth qi referred to replenishable qi gained from breath, food, and so forth. The theory was that the use of post-birth qi reduced the expenditure of pre-birth qi, thus extending an individual's lifespan.
The current diverse definitions of qi are a result of theorization about it by groups and cultures over different time periods. Generally, the disputes about qi arise due to incompatible extensions of the basic theory in different branches of belief. Some other cultures have similar concepts and call them ki (Japan and Okinawa), prana (प्राण) (India), mana (Hawaii), and pneuma (Ancient Greece); a similar concept is also found in Korea and Vietnam, and called simply qi. The Yogic concept of chakras is also related.
There is no scientific evidence for a fundamental force with the properties of "qi". Modern science currently explains all observable phenomena with the fundamental forces of gravitation, electromagnetism, and the strong and weak nuclear forces.
 Amorphous claims
|—Stephen Barrett, Penn & Teller: Bullshit!|
Qi is a complex topic because there are so many different contextual uses for it — many overlapping in certain aspects. In terms of martial arts, some use it as meaning some sort of life energy, some use it as just meaning breath control, and some use it as a paradigm for specific physical techniques.
In terms of spiritual qi, you wouldn't have the same discussion about qi with a dedicated Taoist that you would with an acupuncturist; nor would a practitioner of Traditional Chinese Medicine (which bears slight relation to traditional Chinese medicine) necessarily reference qi in the same way that the Dalai Lama would. Each of these groups have highly specific ideas about what qi is, how it can be used, and how it can be replenished.
This complexity is further enhanced by groups that attempt to interpret historical treatises on qi. The common usage of words changes over the years, and context can vary dramatically based on the society and environment at the time that a particular word was in use. These "unspoken assumptions" have led to various interpretative difficulties concerning historical documents regarding qi. Has your bullshit-detector gone off yet? It should have.
Pre-birth qi, post-birth qi, blood qi, breath qi, heavenly qi and many more are described in a variety of historical Chinese texts over centuries of discussion from a variety of interested parties. As a result, it seems there are as many possible variants of qi as there are interested parties involved in theorizing about it.
Since pre-birth and post-birth qi are the original concepts, it is certainly worth trying to understand how the original theory of qi was created, and why.
 Development of the idea
The observable phenomena leading to the theory of pre/post birth qi were exactly the same phenomena seen everywhere else in the world; in Europe, it led to theories of "vapors", "humors" and so forth. These beliefs led to techniques such as bloodletting, leeching and other "cures". Of course, Christianity had a major influence on the direction the theories followed in Europe as well, which is why illnesses were often attributed to sin.
In China, the same physical observations led to a different conclusion—the fundamental qi paradigm.
The Chinese observed that if you deprive someone of food, [[water] or air for long enough, they will eventually die. This led to the belief that people died because air, food and water were major sources of some other kind of qi—eventually called "post-birth qi". The thinking went that depriving people of those sources of post-birth qi forced their bodies to use pre-birth qi until it was gone… resulting in death. The speed at which deprivation caused death was logically determined to be a direct indication of the concentration of post-birth qi available from the source. Ergo, air was a critical source for post-birth qi—from which came the emphasis and focus on cultivating qi through breathing techniques.
These observations resulted in a Chinese approach to longevity by cultivating post-birth qi and conserving pre-birth qi via breathing techniques, meditation, diet, herbs, acupuncture, sexual abstinence and so on. (Sexual abstinence practices came from the observation that men would "issue their essence" which supposedly contained part of their pre-birth qi. Abstinence supposedly conserved that irreplaceable supply.)
The primary goal was to conserve pre-birth qi by reducing its usage through methods of conservation, coupled with increased substitution of post-birth qi wherever possible. The belief was that while some use of pre-birth qi was unavoidable, the quantity required could be reduced—or even possibly eliminated.
Between this and the "initial" size of the store of pre-birth qi, the Chinese were able to explain why individuals had varying lifespans. When people who didn't practice qi conservation lived a long time, the Chinese rationalized that those individuals had great stores of pre-birth qi to begin with. The goal of many of the so-called Taoist Immortals was to discover a way to eliminate use of pre-birth qi entirely and to subsist on post-birth qi only—hence achieving "immortality".
All sorts of meditations and visualizations were created to "enhance" the efficiency and gathering of qi within the body; the Macrocosmic Orbit, the Microcosmic Orbit, and many forms of qigongs were developed for that purpose.
Later on, of course, the qi paradigm was used to explain illnesses (qi blockages or imbalances opening the body to harm), and so forth. Early acupuncture and herbal treatments (Traditional Chinese Medicine) all center around the idea of removing those blockages and/or imbalances so the body can naturally prevent illness and heal itself.
The idea of qi was a deeply profound and sophisticated concept developed at a time when better information was unavailable. The qi paradigm fit the then-observable phenomena perfectly because it was developed from said observable phenomena… and is therefore logical in spite of being in error.
 In Martial Arts
Many Eastern martial arts have some layer of built-in "qi", somewhere. This is especially noticeable with "soft" styles (ones that place less emphasis on strength and more emphasis on redirecting the enemy's strength). Several well-respected martial artists (for example Lowry) have hypothesized that the developers of martial art styles that emphasize qi knew there was probably no such thing, but used the idea to explain why their techniques worked (essentially, they were applying the idea of the God of the gaps to their techniques), and that their students either didn't realize this, or didn't pass it on, so the ceremonial and spiritual elements that were meant largely as "This is my best guess", ended up basically being dogma. Most modern students (most, not all) either accept that qi is basically a placeholder for things like biomechanics that does explain why martial arts techniques work, or simply do not care. The schools that do place large amounts of emphasis on qi and insist that it's real can be thoroughly ignored.