According to the Turkish linguist Talât Tekin in his book A Grammar of Orkhon Turkic, the root word of Täŋri (Tengri) was Täg- (Teg-) meaning "Turn around" or "Wrap around" (related with some Old and Modern Turkish words such as Teker, Tekerlek, Değiş-, Değirmen, etc) because the sky covers the entire World, looking as if it wraps around it. He proposed that the -g particle in Täg- later turned to a Nasal N (ŋ, ñ, ng) as can be seen in Turkic languages.
Thanks. That's what I thought before and I was in the right direction. Are there other theories?
Also since this Teng, Ting seems to be related with turning and wheels and cogwheels, could we say that the concept of Tengri is also related with human mind or a general mind of infinity itself since the human mind-brain is usually pictured as consisting of wheels and cogwheels just like the motion of universe is circular?
Salim Koca, a Turkish historian from the Gazi University, thinks that it comes from the root word Taŋ (Modern Turkish Tan meaning "Dawn") and the -ri suffix is the same with the -ra suffix that can be seen in the word Soŋra, adding a "Afterwards" meaning - in short, Prof. Koca thinks that Old Turkic Täŋri means "After Dawn", or "Greater Than Sky". However, it's only in Oghuz, Chuvash and some Siberian dialects of Turkic in which Täŋri (Tengri) has back vowels (Taŋrı, Tanrı, Tangara, Turï, etc) - the rest of the Turkic languages have it with frontal vowels (with ä, e, etc). And Prof. Tekin's theory is against the Taŋrï -> Täŋri view.
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Also since this Teng, Ting seems to be related with turning and wheels and cogwheels, could we say that the concept of Tengri is also related with human mind or a general mind of infinity itself since the human mind-brain is usually pictured as consisting of wheels and cogwheels just like the motion of universe is circular?
I don't know.
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Is the word tenggis derived from the same roots as Tengri? Or do they just sound similar?
They might be. I think our member hjernespiser once posted something like that somewhere in this forum.
I am under the impression that we've already discussed this particular topic before, but it is worth noting that those theories which derive the meaning of Tengri/Tangra from roots related to "turning or rotating" seem most plausible. It is quite natural to employ the image of revolving sky as observed in astronomical phenomena (and reproduced in rituals and dances) for rendering notions like "time/fate/deity" or "life-force".
Still even the pseudo-etymologies can be highly suggestive for instance in spiritual practice. Thus I use the name Tengri/Tangra as mantra for meditation thinking the first syllable while inhaling and the second one while exhaling. The former reminds of tïn ("breath", "spirit") and thus represents receiving the "breath of life" (life-force or spirit), while the latter resembles the root arï- ("to purify", hence arïgh - "pure, sacred") meaning that I purify myself while exhaling the exhausted air. Not that Tengri/Tangra has really meant "Sacred Spirit", but it is a nice association to use in meditation practice (or dhikr - "remembering" to use the Sufi term).