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Explanation
The Joke
The comic shows a bearded man standing on the side of a road, hitchhiking with his thumb out. Instead of a sign listing a destination like "Los Angeles" or "New York," his sign reads "Half the remaining distance to my destination." The caption below reads: "So far, the empirical approach to Zeno's Paradox has been inconclusive."
The joke is that the hitchhiker is trying to physically test Zeno's Paradox by only ever traveling half the remaining distance to wherever he is going. Since each ride would only take him halfway to his goal, and the next ride half of that, and so on, he would theoretically never arrive -- the remaining distance keeps halving but never reaches zero.
The Humor
The humor comes from imagining someone taking an ancient philosophical paradox completely literally and trying to test it empirically through hitchhiking. The man's disheveled, long-bearded appearance suggests he has been at this experiment for a very long time, which makes sense -- if each successive ride covers half the remaining distance, his progress would slow to a crawl. The caption's dry observation that the results have been "inconclusive" is the perfect deadpan punchline: of course they are inconclusive, because by design the experiment can never be completed. The comic also plays on the fact that mathematically, an infinite series of halved distances does converge to a finite sum (he would eventually get there), but practically, each ride gets shorter and shorter until no driver would bother stopping.
References
Zeno's Paradox (specifically the Dichotomy Paradox) was formulated by the ancient Greek philosopher Zeno of Elea around 450 BCE. It argues that motion is impossible because to reach any destination, you must first cross half the distance, then half of the remaining distance, and so on infinitely. Mathematically, the paradox was resolved by the development of calculus and the concept of convergent infinite series -- the sum 1/2 + 1/4 + 1/8 + ... equals 1, meaning the traveler does in fact arrive. However, the comic sidesteps this resolution by making each leg a separate hitchhiking ride, which practically would become impossibly short.