上下而求索" is from
《离骚》 (writer:
屈原 qu yuan;derivation:《li sao》)
The whole sentence is "路曼曼其修远兮,吾将上下而求索".
Means:Although the road is endless and faraway, I still want to pursue the truth in the world.
In this sentence, "上下" means sky and earth.
"求索" means to find and pursue.