As dancingalone said, the open hand version changed to a closed fist version in Goju. It was actually Kanryo Higaonna, who had the original and slightly different version , who made that change. Gogen Yamaguchi taught a different version again. The Higaonna version was obviously the first of the Goju ones. It contained the steps forward, a turn, and steps back before another 180 deg turn back to the front. Miyagi took out the turns completely. Yamaguchi put the turns back in but reduced the steps to the rear. Higaonna's version and the version practised in Okinawa today, had a softer style of breathing than you see in Uechi Ryu and Yamaguchi's is like that one too.It would be interesting to note why there are differences between Sanchin kata between the two though. I've never really looked into that. I've 'seen' Goju's version of Sanchin and I 'do' Uechi's version. That's piqued my curiosity. I have a book on Sanchin, mostly Goju version. I'll have to take a look at it again (been many years since I've read it).
As to why? We can only speculate but I doubt we will ever really know. Perhaps it's to do with other aspects of the training that Sanchin reflects. (I think it was Uechi who first made the statement that Sanchin embodied all the training of Pangai-noon. Later the same statement had been adopted by Goju, with good reason.) Uechi Ryu version is more crouching, at least in the earlier versions I have seen, while the Goju versions are all more upright. Uechi Ryu tests by beating the ...t out of you, as does Yamaguchi's while the Okinawan Goju versions are tested for body structure. Also the Uechi version has the two Mawashi Uke to the side while the Goju versions are north/south.
Lots of potential for research if you have the time. I'll look forward to reading your book.
Hard to tell really. It is said that Sanchin is part of the white crane system. Interesting that the part Higaonna and Uechi brought back as Sanchin is so similar. To me it suggests that they either trained in related schools in China even though they were there about 20 years apart or Uechi had a connection with Higaonna when he returned to Okinawa. The closed fist in Goju coincides with the introduction of karate into the schools.Higaonna Morio stated in a Dragon Times article that Miyagi Sensei made the change in Sanchin from nukite strikes to a closed fist among other alterations. Presumably the Uechi-ryu version is less changed from what Higaonna Kanryu taught.
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