How to tell if Blender has crashed? I am unsure whether or not Blender has crashed / stalled.
The screen, especially the timer, haven't changed in over an hour (while usually the timer tells you how much time has elapsed since rendering began).
But I'm thinking, hey, maybe the timer's just slowing down because it's processing and thinking too hard to update?



Is there a way to know? As far as I know, when I hover over the different buttons in the properties panel, they change color (and so does the X for cancelling rendering), so it might just be working (that's what indicates my Activity Monitor as well, as seen in the image below).



But what's a certain way to know whether or not Blender has stalled / crash?
If the interface is still responsive, Blender hasn't crashed (yet). But in this case is engaged on some heavy computing.

In this case the issue is that you are trying to render using an insane number of samples!

You've set up 1000 samples but have the square samples box enabled, that will make the number 1,000,000 (1000 samples x 1000). 



A million samples will require massive computing power!

Uncheck the square samples box and bring the number of samples to a reasonable number...