Well, you can find the sempi's opinions in his glossary:
http://www.shinjinbukan.com/dictionary_T.html#tenshin
転身
てんしん
tenshin
Glossary Category: Okinawa Karate Dō/Techniques , Shinjinbukan/Syllabus
Lit. Change direction or course. Tenshin is one of the three basic elements of Okinawa Ti. It is used to generate an effortless and powerful body movement and acceleration. One of the trademarks of the Shinjinbukan School is the use of tenshin to create an immense thrust for each tsuki (hand strike) & keri (foot strike).
Tenshin is commonly defined as "Body Displacement". This is a very superficial definition, because tenshin is more than just moving from point A to point B. Tenshin could be compared to the breath of life: "Without air, we can't live. And without tenshin we can't move or use our body efficiently". In fact, tenshin is directly connected to the use breathing techniques. Therefore, a more wholistic definition of tenshin would be: "The most efficient method of body mechanics used to generate body movement".
Furthermore, according to Onaga Kaichō, "Our bodies do not move back and forth, but left or right." The reasoning behind this approach is that we do not have four legs. So, we do not have front legs or back legs, we only have left and right.
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http://www.shinjinbukan.com/dictionary_T.html#ti
手
ティー
Ti
Glossary Category: Shinjinbukan/System
Lit. Hand(s). Pronounced Tchi. The ancient indigenous Okinawan martial art from which preceded modern karate. Ti is the essence of Karate and the foundation of the Shinjinbukan curriculum.
See Te , Shuri Te , Shuri Ti , Sui Di , Naha Te , Nafua Te , Naha Ti , Nafua Ti , Tomari Te , Tomari Ti
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手組
ティー グミ
Ti Gumi
Glossary Category: Shinjinbukan/System
Lit. Sparring. The term Ti Gumi is "suggested" for use with beginner students in order to move away from Kumite by introducing basic ideas from Kakie and Iri Kumi. My basic (simple) definition of Ti Gumi is "A type of Ippon Kumite confined within three concentric circles of approximately 3, 2 and 1 meters in diameter. Ti Gumi only begins once the two opponents hook their arms from any of the three basic points of contact:
1) Inner wrist contact
2) Palm forward hooking from the outside wrist
3) Palm forward hooking from the inside wrist"
What is the historical context to use the term Ti Gumi? In the early 20th century, several authors described a free-style sparring in Okinawan Karate with the term Ti Gumi. In Uchinaguchi (the Okinawan dialect), the word Ti Gumi is written with the same Kanji (Chinese characters) as Kumite, but in reverse order.
Why use Ti Gumi? Modern sports Karate is focused on tournament fighting and kata competitions, with no real integration of the muscle mechanics or the curriculum. On the contrary, the Shinjinbukan curriculum integrates Ti into all aspects of training: conditioning, katas, machiwara, etc. This integration is essential in the study and application of Kakie and Iri Kumi. However, this could be too difficult to achieve even with the guidance of a qualified teacher. Therefore, Ti Gumi could be used as a teaching method for beginners and instructors from other styles who need to bridge the gap between sports Karate and pure Ti.
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手術
ティージュツ
Ti Jutsu
Glossary Category: Okinawa Karate Dō/Ryūha
Lit. The Art or skill of the hand. Ti Jutsu is a generic term used during the early 20th century, when the term Karate had not yet been adopted by the Okinawans.
See Tōdi
唐手
トゥデ
Tōde (alt. Tode, Toude)
Glossary Category: Okinawa Karate Dō/Ryūha
Lit. The Tang (China) hand.
See Tōdi
唐手術
トデジュツ
Tōde Jutsu (alt. Tode Jutsu, Toude Jutsu)
Glossary Category: Okinawa Karate Dō/Ryūha
Lit. The Art or skill of the Tang (China) hand.
See Tōdi
唐手
トゥーディ
Tōdi (alt. Toudi, Todi)
Glossary Category: Okinawa Karate Dō/Ryūha
Lit. The Tang (China) hand. The Okinawans used the term Tōdi instead of Karate before their martial arts was introduced to mainland Japan. Since the word Tōdi means Chinese Hand, it had to be changed to the name karate, using more “modern” characters: 空手. This was more than a departure in terminology, but part of the standarization and cultural changes of the Meiji Period (1868 — 1912). These socio-political changes brought Okinawan culture & government under Japan and away from China's sphere of influence.