Asperity
Part of speech: noun
Definition: Roughness as of stone or weather. Something that is harsh and hard to endure. Harshness, as of temper. A part of a geological fault line that does not move. Earthquakes begin and end at asperities.
Sharpness
Part of speech: noun
Definition: the cutting ability of an edge; keennessthe fineness of the point a pointed objectThe product or result of being sharp.pungency or aciditydistinctness, focusacuteness or acuity
Example sentence: 'Tis the sharpness of our mind that gives the edge to our pains and pleasures.