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.

  • Euripides mentions Hydra regenerating its heads in Herakles, but I don't think he explicitly tells us that she grew two new heads for each lost one. I think the oldest known source for that is Diodorus (4.11.5).
    – yannis
    Mar 14, 2017 at 17:31
  • @yannis I was reading through the Euripides to confirm when I got really busy. (Wasn't able to find the passage on simple search, but I am interested in the original wording.)
    – DukeZhou
    Mar 22, 2017 at 14:06


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