My sensei was explaining something, and made a comparison “like connecting a bamboo to a tree.” I was stumped (pun intended?), and was not really sure what he was trying to say. So I asked what does he mean by this exactly? So it was explained to me as follows.
「木に竹を接ぐ 」 “ki ni take wo tsugu”
literal meaning: to connect (graft) a bamboo to a tree.*
There is a teaching in Japanese about connecting a bamboo branch onto a tree. That it means there various ideas being done, but in the wrong ways. So that is to say, instead you should attach a branch of a tree to the trunk of a tree, not a branch of bamboo as they are incompatible. The meaning is that it is inharmonious and unreasonable to try to graft bamboo branches to a tree trunk, so in turn, this phrase can be used to indicate something inharmonious, unreasonable, useless, or even just inconsistent.
Some people say it is equivalent in English to say “to mix fire with water,” but I feel that this is not quite right. The meaning seems a bit more subtle than that to me. I also saw it compared to another more disturbing turn of phrase (supposedly English) “to sew a fox’s skin to the lion’s.” Needless to say, I have never heard this phrase before.
*Note: I prefer the word “connect” over “graft” for this proverb as to me it sounds a bit more poetic somehow. Connect is also the more literal translation of “tsugu” so I feel it is fitting, though in English the best word is actually “graft.”