1)
What does this Mizmor discuss?
1.
Malbim: It discusses knowledge and Hashgachah.
2)
What is the meaning of "Chakartani va'Teda"?
1.
Radak: You investigated my heart and know it. This is like "Ani Hashem Choker Lev Bochen Kelayos" (Yirmeyah 17:10).
2.
Malbim: There are two ways in which You know man. Based on man's understanding, they are contradictory. (a) You know from the beginning everything that will happen. This does not depend on time, place and possibilities - "va'Teda". (b) Man has free choice about his deeds. You investigated to know what I chose. The first knowledge leaves different possibilities for choice; this is above man's understanding.