So after discovering last night that indeed there still is a nest on my balcony - just re-located to be out of view from my window - I decided today, since it's hot, to put out some water for the bird.
I draw the line at feeding the birds - its mate, if it's still out there, can always fly in food - but water I can spare. It can't be easy, sitting in one place all day without easy access to a drink.
The Mama pigeon immediately took off when I opened the screen, leaving her "nest," such as it is, vacant. At first, it looked like there wasn't much in it, but after a minute I could spot the baby pigeon, lying helplessly on its back, eyes shut, legs up, looking pretty much like a little sausage with yellow down on it. It was wiggling around a little, helpless, none too comfortable. Hard to be entirely unmoved by the so-called miracle of life happening right before my eyes on my balcony.
There's only the one - one of the two eggs she laid must indeed have rolled off the edge; her nest is definitely in a bit of a shambles compared to what I previously saw. I couldn't resist taking one photo. The Mama came back shortly after and is resuming her position, and as yet remains skeptical about the water, but I suspect that won't last long. Click on the photo for a slightly larger version - its head is tilted away from the camera, so you can see the eye and the beak (both grey).