How do you take the enormous amount of critical information gathered every day by city agencies and make it actually useful to citizens? On the City of New York’s DataMine web site, just looking through the list of datasets generated by the Department of Transportation alone is enough to give you a headache. Enter the annual NYC Big Apps competition – a call to software developers who can mine this data and find ingenious ways to put it at the fingertips, or keyboard clicks, of the average New Yorker. This April, winners received a total of $20,000 in cash, the wide exposure their work deserves, investment meetings with BMW, and a chance to talk to Mayor Bloomberg about their ideas…