I am referring to Zeno of Elia (c.490 –c.430 BCE) and his famous Dichotomy Paradox. This paradox has to do with infinite divisions based on 1/2.
It seems to be that the conception of the Hydra as growing two heads for every one that is severed occurs only after Zeno. (This is a reverse of his paradox, in the form of infinite expansion through doubling.)
This new conception of the Hydra is attributed to Euripides (c.480 – c.406 BCE). Although I am having trouble locating the exact passage at the moment, it does re-occur some centuries later with Pseudo-Apollodorus, Bibliotheca 2. 77 - 80.
Is there any evidence that Zeno influenced this new conception of the Hydra, by suggesting the underlying mathematics of the narrative gimmick?
I suspect not, but if there is an example of this conception of the Hydra before the fifth century, it would disprove the connection.
