As a sidenote to Danny's answer, there is an interesting story with R' Tam and his brother Rashbam, recounted by the Mordechai (Additions to Eiruvin end of 1st perek). The Rashbam being ever so modest, pious and carful would not raise his eyes while walking in the street. Unknowingly the Rashbam ascended a wagon that was harnessed to a horse and donkey (or mule), which Jewish law forbids to ride on (kilayim). Luckily, his brother R' Tam passed by and noticed what was going on and said to his brother in Hebrew,
"אל תהי צדיק הרבה, שא מרום עיניך, והנה סוס ופרד לקראתך"
"Do not be overly pious, raise your eyes to the heavens, behold there
is a horse and a mule in front of you."
Apparently the R' Tam mocked his brother for being overly pious by looking down and not being aware of his surroundings, which instead of preventing him from sin almost brought him more trouble than protection.