I think Peacegirl will still need some kind of simplified diagram or picture to follow what is being said. (And even then she'll just have to flatly deny it or appeal to mysterious unknown factors once she gets it.) Anyway, I'll give it a shot...
Peacegirl, imagine that we want to send a rocket to planet

. This planet is moving across the sky from left to right, across the points represented by letters below:
<- A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T ->
At time T1 we look at the planet and see it at point B, like so:
<- A -

- C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T ->
Bob is a lessanologist and proponent of real-time efferent vision, so he assumes that the planet really is at B at T1. He calculates how far the planet will travel across the sky while the rocket travels to get there, and works out that

will cover ten letter-points during this travel time. So Bob fires his rocket towards point L.
Jim is a normal person and proponent of delayed afferent vision, so he assumes that what he sees at T1 is a dated image and that the planet only
appears to be at B at T1, while it is
really at point E. So Jim also calculates how far the planet will travel while his rocket is in flight -
using the exact same calculation for this as Bob - and also determines that

will cover ten letter-points during this travel time. But because he believes that the planet is at E rather than B at T1, he aims his rocket towards point O instead of point L like Bob.
Bob understands the situation like this:
<- A -

- C - D - E - F - G - H - I - J - K -
L - M - N - O - P - Q - R - S - T ->
Point B is both the perceived and actual position of

at T1, and point L is where he aims his rocket.
Jim understands the situation like this:
<- A -

- C - D -

- F - G - H - I - J - K -
L - M - N -
O - P - Q - R - S - T ->
Point B is only the
apparent position of the planet at T1 which is
really at E, so he aims his rocket at Point O instead of point L.
When they fire their rockets, guess what happens. Jim's rocket arrives at the planet while Bob's rocket does not. Both use the exact same calculations. The only difference is that Bob takes his perception of the planet's location at T1 to be real-time, while Jim takes it to be dated. Yet it turns out that Jim was right, and both Bob and Lessans were wrong.