Sadly, Futurama is ending, again. Since the entire series is available on Netflix, I’m trying to catch up on any episodes I may have missed. What I love about the show, in addition to the trenchant parodies of sci-fi, are some of the most advanced math ever to appear on mainstream TV. For example, the main plot of the episode Prisoner of Benda hinges on an new mathematical theorem created by the writer Ken Keeler, who has a Ph.D. in applied mathematics from Harvard.
In fact, many of the show’s writers have math and science backgrounds, and sprinkle in references liberally. Sometimes, classic philosophical puzzles also feature prominently. For example, in the Six Million Dollar Mon, Hermes incrementally upgrades his body with cybernetic implants, while Zoidberg keeps the discarded human parts for a ventriloquist’s dummy. The writers cleverly bring up the logical paradox usually called the Ship of Theseus: If you take a single plank from a boat and replace it with an identical one, almost everyone would agree that it is the “same” boat as before. But if you keep repeating this process, you can end up with a boat that consists of none of the “original” planks. Even worse, if you take all the discarded planks and build a second, identical boat, which of the two is the “real” one? Far from being a game of semantics, this process really occurs during biological processes like DNA replication, prion diseases, and the ability of amoebae to move by breaking down and rebuilding actin filaments in their cytoskeleton.
In our digital world, computer files are copied and the originals overwritten almost constantly. We readily say that the file is the same, referring to the information as opposed to the physical bits. More speculatively, the transporter in Star Trek essentially obliterates the person being transported and recreates him or her somewhere else. Yes, very few people in the Star Trek universe refuse to use the transporter for this reason (see also the duplicating machine in the film “The Prestige“).
Perhaps this is the way we should think about life, or replicating crystals, in general. We should focus on the self-replicating information, as opposed to the particular physical realization.