And my understanding is that we got punched cards of that size because they fit into the boxes and drawers for large-format US banknotes:

http://en.wikipedia.org/wiki/Large-sized_note

Which in turn apparently goes back to taking a common paper size and cutting it into reasonably-sized pieces:

http://ask.metafilter.com/262846/What-is-the-origin-of-the-d...

So apparently one person lost to history said, "How big should it be? I don't know. Maybe about this big?" Centuries later, somebody at IBM said, "It looks like we could fit 80 columns on that. Good enough?"

Hollerith cards originally had 45 columns.

Line length around 80 columns come from letter paper in a typewriter (via teleprinters) which in turn comes from book printing, where around 60–65 printed characters (plus blanks) were established as most readable centuries ago.

80 columns gives you 3 files side-by-side on a 1920 monitor.

Surely that depends on more than just the number of columns and the number of pixels.