Meaning of "educating the ice"

Solution 1:

I think it's a mistake to look for a way for that sentence to make sense. I would say instead that it's supposed not to make much sense.

Evidently the narration is in a very close third-person point of view, and it's describing the character's actions with the words he would use himself -- and in this case it seems clear that it's words he actually thinks.

The borderline-nonsensical choice of "educate" serves to characterize the character as an alcoholic who's trying to tell himself he's not. He's pouring vodka over the ice, but he's pretending that he's doing that to do the ice a favor (education is a good thing!), rather than drinking because he's addicted.

The bizarre phrasing also lets him feel clever about having invented such a colorful metaphor (and clever people are too smart to let themselves slide into alcoholism; he's clever; ergo he's not an alcoholic. Phew!)

The metaphor isn't really all that clever (for one thing, it doesn't make sense), but he's already drunk enough to be unable to see that.

Solution 2:

As Jason said in a comment, "educated" is being used metaphorically. Here's what the sentence means:

Before returning to the back deck he improved the ice in his glass once more with vodka.

Solution 3:

The meaning is certainly that he added more vodka to the remaining ice in the glass.

The use of the word educate is interesting. The only vaguely-related definition I could find is listed as obsolete in OED. The entry was updated in 2012 and the last citation for this usage is from 1806.

†b. To bring up, look after, or rear (a child or animal) with respect to food and other physical needs. Obsolete.

The usage is transferred to the inanimate ice, which presumably is thought of as having a physical need for vodka similar to his own.