When you turn the laserpen, or whatever, in your hand, I imagine the laser beam a meter in front of you moves at distance X.
But the laser beam's end moves from position right-of-moon to left-of-moon at the relative speed as a meter in front of you. Ergo, doesn't the light at the end of the laser speed across the surface of the moon faster than light?
In retrospect, no. It would just take time, at the speed of light, to move across the surface of the moon - bending the laser beam...
...As you said, with the hosepipe.
You sneaky dwarf, you.
Yerbutnobut.
Flicking the pen
does send the "end spot" across the moon at FTL speeds. Except that the time for the "movement to start/finish" from your initial motion takes the expected distance that a SoL-type of communication would take
from where you are.
It's a superluminal track, indeed, but it conveys no information along its length, and takes standard SoL time (from you, the origin) to even happen..
That's what the hosepipe idea shows. Two things could become wet within moments of each other (even though the water could never have physically gone from one of the things to the other in such a time, given whatever physical constraints you lay upon that jet of water), but the water is coming from
you, and only reaches either/both of them as fast as the water
does go. It's different bits of water for each. And you might well have switched the water-flow on or off as it was being aimed towards either target, but if the presence/absence of water was the only information each would have, they wouldn't have any way of knowing if the other was getting wet, or if the other
wanted to get wet, erected an umbrella, etc. The "end of the beam", or where the water splashes, just happens to be a description of a continually renewed and independent bit of
your transmission, and is not something that can be given a state to 'hold'.
(I deleted a whole "lighthouse illuminating targets at each end of the universe" set of paragraphs above that para. The above was originally the "TL;DR;" conclusion, but became long enough in its own right and said everything I wanted to as well. Still too long, probably.)
[1] Ignoring the expansion that will be happening, yadayadayada. Let's just say we have targets set 14 billion LY away, assumed to be in an equivalent frame of reference (which means they're not 'stationary' to the 'local' frame of reference, just as translated from the origin, etc) and forget about the whole expansion issue.