Manhattan...."island"?

OK, this is where I am clueless. I'm looking at this map of Manhattan island, and I'm wondering how the hell it's an island? Where's the water on the other side? Not being totally hopeless, I decided that maybe, like other parts of the world like chicago, mumbai, and Amsterdam, the water was artificially built up, making what was once an island into part of the mainland.

I could save face by hiding my ignorance and finding the answer on the internet. But what's the fun in pretending to know everything?
.......

Ok, so it's an "island" because of the Harlem River? I think that's cheating....