Two thousand years ago, wise men of this world weren't lucky enough to have GPS. In the Christmas story, then, the wise men chose to follow a star to navigate their way to Bethlehem—but, scientifically speaking, would that really have worked?
Fortunately, Randall Munroe of XKCD has taken a look at the problem. As he explains, the main difficulty in working out whether those men were as wise as their name suggests is identifying exactly what they were following:
It's tricky to figure out exactly what the wise men would have been following. There aren't very many good astronomical candidates for the Star of Bethlehem (Chinese records don't show a supernova at the right time, and none of the other obvious candidates check out) and, furthermore, there's a lot of historical and theological debate over Jesus's date of birth ("4 BC" seems to be the closest thing to a historical consensus date). These charts are all calculated for a somewhat arbitrary departure date from Jerusalem of December 25th, 1 AD; different departure days would lead to different paths, but the overall picture would be the same.
Particularly prominent in the night sky are planets. Hardly traditional, admittedly, but it's likely they'd have provided good markers to follow. Munroe has sketched out the paths the men would have taken if they'd followed Venus (left) and Mars (right).
Neither look particularly promising. Instead, then, Munroe tried out a star. If the wise men had followed Sirius—the brightest star in the night sky—day and night, even when it was below the horizon, they'd have spiraled off south, eventually going in an endless circle, 30 kilometers in diameter, around the South Pole.
The other option—just jounreying by night to ensure travel was always in the direction of the star—would've taken them on a southerly path that just skirted Bethlehem but ultimately landed them in Botswana.
In other words, they could've ended up next to the manger—but it would have been as much through luck as judgment. [What If?]