I am the Kat that Walks By Itself

Yeah, I know how to create a seamless mobius scarf in crochet - you crochet the first row flat, then join it in a loop with a half-twist and keep crocheting. But I don't think it's possible with a normal knitting loom. (And I'm suspecting that it simply isn't possible with any kind of knitting loom). With needle-knitting I expect one could do it with circular needles, but I don't needle-knit.