According to Zielinski's Law the ancient poets told simultaneous events chronologically without moving back and forth in time.
Did Homer and Hesiod not have a way to say 'meanwhile'?
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You absolutely could say "meanwhile" in ancient Greek. It's not a matter of what words to use, but of the narrative practice of oral poetry. The problem is that Zielinski and some immediately after him preceded the major discoveries of the orality of Homeric poetry. Zielinski was writing at the turn of the century, and still considered the Homeric poems primarily written. Meanwhile, Milman Parry wasn't even born until a couple years after Zielinski formulated his law.
What's actually going on is summarized by R. M. Frazer:
Zielinski explained his law as due to the poet's habit of describing events as an observer; observation always proceeds forward in time and it is only by means of analysis that we are able to synchronize events. Frankel gave another explanation: the poet lacked the abstract idea of time into which different actions might be integrated.
It seems likely, however, that Zielinski's law is best explained as a law of oral poetry, the study of which came into prominence after Zielinski and Frankel wrote. Simultaneous events are told consecutively, or paratactically, and the paratactic method of composition is one of the most important techniques of oral poetry. This method has been well described by Notopoulos, though without any reference to Zielinski's law: the oral poet strings events together, one after the other, connecting them by means of foreshadowing, retrospection, and ring-composition.
Hesiod’s Titanomachy as an Illustration of Zielinski’s Law, R. M. Frazer
It should be noted that not everyone agrees with Zielinski's law. A good rundown of the problems in interpretation can be found in Ruth Scodel's 2008 article, "Zielinski's Law Reconsidered," published in TAPA 138: 107–125.