John,

Obviously you can have neither a 100% efficent antenna nor a 150%
efficient antenna. That doesn't change the definition of efficiency.
That was my point. It doesn't matter if you're talking about possible
or impossible antennas, efficiency is power out divided by power in.

Also, yes, a dipole has directional characteristics, but it would seem
that Art is talking about something more directional than a dipole that
is not a multielement array, and he asks us to imagine a dipole with
inherent directional capabilities

This suggests that it doesn't have the familar dipole directionality,
but something else.

What is that something else? How does it bear upon efficiency?

Dan