Indrajala wrote:In the seventh century they developed simultaneously, but bear in mind that Huayan was centered in Chang'an amongst the aristocracy while Tiantai initially was provincial. Tiantai eventually in part moved into the city.
It would seem to me that Tiantai had less of an impact on Huayan because of the regional and perhaps class differences. It seems to me, as well, that Tiantai included strong yogic elements, whereas Huayan was much more scholastic and concerned with exegesis. Tiantai from the started placed equal emphasis on meditation and the study of doctrine.
Both schools of course influenced Chan. Zongmi the Huayan patriarch was in fact also counted as a Chan patriarch. However, in my reading of Fazang's works, I don't seem to recall him making many references to Zhiyi's works, if any.
See these works:
Tsung-Mi and the Sinification of Buddhism
Inquiry Into the Origin of Humanity: An Annotated Translation of Tsung-Mi's Yuan Jen Lun with a Modern Commentary
Entry Into the Inconceivable: An Introduction to Hua-Yen Buddhism
Seeing through Zen: Encounter, Transformation, and Genealogy in Chinese Chan Buddhism
Your questions are rather huge, but I think these works would shed much light on them.
But keep in mind there is the Buddhism of the Tang period and then there is the Song and post-Song developments. Tiantai as a form of scholarship in China (rather than a community) exists even today, but that can't be said of Huayan minus the new group based out of Taiwan. Post-Tang a lot of Zhiyi's works were studied quite extensively as foundational works.
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