In your example you're using the term "now". That term already implies a point in time and therfore an infinitely divisible time. The problem is that while you certainly could conceive of a half planck time you could never locate that half in time. I.e. an event does not happen at a point in time. It happens anywhere in a given range of time with at least the planck length in extend. Now suppose that event A happens anywhere in a given timeslice and event B happens in another timeslice that starts half a planck time after the slice of event A. You can not say that event B happens half a planck time after event A since the timeslices overlap and thus you cannot even say that event B happens at all after event A. It might be the other way round. So while in your mind this half planck length seems to have some meaning in reality it does not. Your mind insists on visualizing time as continuous and therefore you can't easily get rid of the feeling that it were.
Why do you say that the time slices overlap? It seems on your set up, and mine, that they do not. The point seems to be just that nothing can happen in less than a Planck time, not that something cannot happen in 10.5 Planck times. The latter doesn't follow from the former so far as I can see. But I'm not on firm ground here, and I may well be mistaken. (ETA: But at any rate my example above doesn't involve anything happening in 10.5 Planck times. Everything I describe in that example can be said to occur in a whole number of planck times.)
And 'now' doesn'... (read more)