Is it considered a sin not to lower one's gaze from girls or women, even if the gaze is ordinary and devoid of lust, and how does such a gaze affect memorization and the pursuit of knowledge if it is a sin?

In determining what is lawful (halal (definition)) and unlawful (haram (definition)), one must refer to the infallible texts of Islamic law. It is not permissible for a person to employ his intellect in objection, for this is the path of the disbelievers. Allah has forbidden men from looking at women, whether with lust or without lust. This prohibition, according to the preponderant view among scholars, encompasses the entire body of a woman. The preponderant view also holds that looking at the face and hands is likewise forbidden. As for the effect of looking at the ability to memorize and comprehend, this is among the punishments Allah inflicts upon the disobedient.