The photo above shows my cat Roo being quite curious about a new item in the house: balloons.

Friend or foe? Alive or not? Anything to do with food? Any threat? I am sure these were some of the questions Roo sorted out for himself, and after about ten minutes, he left the balloons in peace.

Now the word curiosity itself is interesting. After reviewing the Oxford English 
Dictionary, we see its initial use revolved around attention to detail:

Carefulness, the application of care or attention. Obsolete.
c1430 Freemasonry 32 He that lernede best..And passud hys felows yn curyste.

Followed later by how most of use it today—a desire to learn:

In a neutral or good sense: The desire or inclination to know or learn about anything, esp. what is novel or strange; a feeling of interest leading one to inquire about anything.
1853 C. Brontë Villette I. xiv. 287 Your curiosity is roused at last.

In a physician, either one is fine, but if you are unfortunate to run across one who lacks curiosity, then do your best to keep your distance, because curiosity is excellence’s sister.