The Sharingan makes the user able to follow the target better, which shortens the reaction time of the user. Does the Sharingan make your mind think faster as well?  

If it doesn't, the users mind should not be able to keep up with what the Sharingan is able to see. If the mind becomes faster, then the user would become a super genius.

Or is there simply no logic at all?

Naruto has recently learned the flash ability from his father Minato. When someone uses flash are they teleporting or just moving really fast?

Additionally, could any form of the Sharingan "keep up" visually with the "flash ability" of either Naruto or Minato?