A dictionary of Confusable Phrases: More Than 10,000 Idioms and Collocations

wise in something • wise to something
wise in something —showing wisdom and good judgment in
smth.: He was very wise in his rulings and tried to govern all
his people equally and fairly.
wise to something —informed about smth.; being aware of
smth.: I’m wise to the fact that he [comedian] dips in the
Farmers’ Almanac for his comedy stuff.
wise men of Gotham • wise men of the East
wise men of Gotham—(UK ironic) fools; simpletons: “I
would pay no attention,” I replied, “to the wishes of those few
wise men of Gotham who would arbitrate this matter.”
Note: 
The expression is unrelated in meaning to the phrase
Gotham City
—(U.S.) a nickname for New York City: I figured
the one place he’d never find me would be Gotham City …
the home of the hated Yankees.
wise men of the East—(the Bible) the three Magi who came
from the East, bringing offerings to the infant Christ: It is
chronicled in an old Armenian myth that the wise men of the
East were none other than the three sons of Noe.
See also: wise guy / wise man.
wise someone up • wise up to someone
wise someone up —(sl.) instruct a person about smth.; give
smb. information: Let me wise you up about the way we do
things around here.
wise up to someone —(sl.) figure out a person: It’s time you
wised up to John and what he has been doing.
with a single eye to something • with one eye on
something
with a single eye to something —exclusively concerned with
or concentrating on smth.: His predecessors are the only
Roman emperors who can be said to have ruled with a single
eye to the welfare of their subjects.
with one eye on something —(also: with half an eye on some-
thing ) 
1
. directing one’s attention only partly to smth. (while
preoccupied with smth. else): She sat at the head of the table
stirring her tea, with one eye on baby Paul, who was fretful
in his little chair. 2. simultaneously thinking about or preoc-
cupied with smth.: He still told jokes, but they were the jokes
of a man who couldn’t see anything funny any more, the jokes
of a man with one eye on the door.