A kwan, by definition is a constellation of people brought together by a shared goal and who likewise share an agreement on the venue or method for attaining that goal. It is not a "style" or a "gym" or a "ryu". A kwan need not reflect a martial background, and, in fact, for many years reflected either a political or intellectual approach. Some of the earliest kwans were little more than poetry sessions over tea. They came to the forefront during the Japanese Occupation as political movements to resist Japanese domination. Following the Second WW the term has come to be used quite a bit with the promotion of Korean martial arts.
".....If you are talking non linear, why are there schools today or do Korean schools trace thier lineage?..."
Fact is that people do a lot of dumb things, and nobody knows exactly why. Why do people use the term "supreme grandmaster" and "grandmaster" when there are no such positions in Korean culture? Why do people continue to use terms like "do-ju" and "do-ju-nim" when it is painfully apparent that these terms are derived from Japanese tradition rather than Korean? Why do Koreans espouse a hatred of Japanese culture and injury during the 20th century while continuing to use structures such as the dan/kyu (aka dan/guep) ranking system and the practice of Aikido, Judo and Kumdo in preference to Korean arts such as Hapkido, Ssireum, Taek Kyon, Archery, and Ship Pal Gi? Why is it that the Koreans have a culture that goes back 3-4 thousand years, and yet their own people do little to maintain or promote their culture, choosing instead to promote the same shallow Western pursuits as here in the States. Its not because there is no history. There is plenty written down and there for the investigation. Its not because it can't be found. If a simple 4th dan from the Midwest can pursue such research whats holding the Korean nationals back?
The simple fact is that by establishing a lineage after the fashion of the Japanese Ryu an entrepeneur increases the chances that monies for seminars, certification and enrollment will funnel to ones' own door rather than anothers'. There is no historical provenence for the sort of lineages that one sees' touted in the media, magazines or books; not in Korea anyhow. In my own case I can trace my lineage--- if you want to call it that--- back to Yong Sul Choi. What does it mean? Little more than if I wish to, I can validate my students through my teacher by getting paper with his signature on it and in this way one of my students can claim a historical relationship with Choi. Whatever winds yer clock. As a Buddhist I have as much having taken my Precepts and now stand as yet the next generation of Buddhists after the founder of the monastery to which I belong. Meaning?
Now since I have gone this far, let me also say what this stuff is NOT.
Being a martial artist does not, in our modern day, mean that a person practices a martial science. It does not mean that one adheres to or espouses a martial code as a premise for ones' conduct. It does not mean that one practices the material used historically by Korean warriors, nor conducts their lives according to a code after the fashion in which they did. Martial arts in the context of todays experience means to use a buzzword or group of buzzwords, antics, dress or structure that suggests an image to ones' community. It is a commercial experience in which designated authorities sell various roles for people to put on. It is what I call "martial theatre". Nothing wrong with that, actually, until one decides to fall back on such theatre as though it were something more authentic. Then, it simply will not hold up. Nobody says people can't put on uniforms, do Okinawan kata, wave around Chinese staffs, use Japanese structure and what-not. All I am asking is that folks not confuse somebodys' imaginings about Korean martial culture with the historical reality. Hope this is of some help, FWIW.
Best Wishes,
Bruce