New Year’s cartoons have always confused me a little.

On the surface, they seem simple enough: Baby New Year, a plump and eerily precocious infant, confronts Father Time, a skinny old geezer with a sickle. Somewhere in the frame, either in the old guy’s gnarled fingers, or in his lap, or hanging on a wall, there’ll be a timepiece — a watch, an hourglass, or the face of a big clock.

There are infinite comic variations, but the underlying message is always the same: out with the old year; in with the new.

The fact that Baby New Year sports a banner like some kind of pageant contestant is somewhat strange, but you go with it, because otherwise how would you know the date of the incoming year?

Then again, since when do babies wear top hats? And how is it that this brand-new baby knows how to walk — or even run — much less clock in to his new job?

Father Time is equally puzzling. Known in any other context as Death, the Grim Reaper, Father Time is frequently softened by cartoonists and illustrators. His face is kindly, not skeletal, and he doesn’t wear a black hood. Also, if you look closely, his sickle is often depicted upside down; in other words, with the blade down by his ankles, not by his shoulder, poised for the harvest of souls.

Often as not, he looks exhausted and gloomy, possibly because this time, the joke’s on him: in the New Year’s scenario, he’s the one getting reaped!

The welter of symbols — baby, reaper, hourglass, top hat, sickle — isn’t too surprising once you realize that Baby New Year and Father Time, like most holiday personifications, represent a kind of cultural hodgepodge.

To understand where they came from, you need to start with the calendar itself. We can thank the Ancient Romans and their innovative Julian calendar, the ancestor of the Gregorian calendar that we use today, for the idea of ending the year on December 31st, and starting the new one on January 1st.

The other calendars of the ancient world were more closely aligned with the growing season; the new year began not in the dead of winter, but instead at the beginning of spring.

One of the springtime new year’s traditions in Ancient Greece was apparently to parade a baby into the fields in order to bless them for a bountiful harvest. This baby — who may or may not have worn a banner — was meant to be a personification of Dionysus, the wild fun-loving god of the grape, and whose mythological birth story involved being born twice: once prematurely from his mortal mother’s womb; and then a second time from the thigh of Zeus, in which he was carried to term. The theme of double birth, or rebirth, made Dionysus — and the no doubt squalling infant who represented him — perfect symbols of optimism and growth.

The precise history is somewhat murky, but it seems that the association of a baby with the new year survived the shifting of new year’s day from March to January. The Catholic Church apparently played a role in the perpetuation of the new year’s baby. After initially suppressing the symbol as too “pagan,” the Church ultimately accepted it as a representation of the Baby Jesus, and thus an extension of the Christmas season.

The confusion over Father Time dates back to Ancient Greece as well. To the Greeks, the personification of Time was a god named Chronos, whose name you may recognize as the root of many of our time-words, such as “chronology” and “chronograph.” Whether by linguistic accident or cultural design, the god Chronos eventually became associated with a similar-sounding deity, the Titan Cronus. Ancient representations of Cronus commonly included a sickle, the tool he used, in Greek mythology, to castrate his father Uranus, and which ultimately became the symbol of his role as harvest god.

Thus the wires were crossed: Chronos, the time god, merged with Cronus, the harvest god, resulting in our own latter-day Father Time, with his sickle and hourglass. His other avatar, the Grim Reaper, also represents a crossroads of time and harvest: he is the god who appears to collect a mortal’s soul when he has literally run out of time.

Baby New Year and Father Time can be found in artwork from the Middle Ages onward, but their expression in American culture was shaped — and some would say, perfected — by the great early 20th century illustrator J.C. Leyendecker, who was Norman Rockwell’s most important artistic influence. Every year, starting in 1906, and running into the 1940s, Leyendecker created a “Baby New Year” cover for the Saturday Evening Post.

It’s worth looking up these images, both for their sheer artistry and for insight into the nation’s preoccupations in any given year, be it war, taxes, politics, or the economy.

And while you’re Googling Leyendecker, see if you can find out what’s up with Baby New Year’s top hat. I looked pretty hard for an explanation, and came up with nothing.

Please drop me a line if you have any luck. Solving that pesky riddle would be a great way to start 2014.