chris wrote:

Why (or how) does the
longer
element "reflect" the radio wave,

A reflector does not reflect anything. It reradiates.

When a element is self-resonant it reradiates with 180 degree phase
inversion.

Spacing from the driven element causes a phase delay. Lets say that
spacing is 90 degrees.

The phase to the rear direction would be -90+180=+90 degrees. Two
elements like this, when phased and in-line, fire in the direction of
lagging current. So the antenna fires towards the driven element.

and the shorter element "direct" the
radio wave.

The shorter element doesn't direct. It reradiates energy. When we
shorten an element and excite it with an external field, the current is
advanced some amount in phase besides having the 180 inversion caused
by reradiating an external field. Let's say we shorten it enough that
the phase advances 120 degrees from the shortening, and we have 45
degree spacing.

Now we have -45 (spacing delay) plus 180 flip (reradiation) = +135
degrees. To that we add another +120 because the element is short and
capacitive. That's +255 degrees. +255 is the same as -105 degrees, and
again since the elements fire in the direction of lagging currents the
driven element's energy is reenforced in the direction of the short
element.

Sorry you asked? Well, that's how it works.

Also, on many multi-element Yagi designs, the norm seems to be just one
reflector, and many director elements. Does this mean that the
reflector is more "effective" than the directors at modifying the
radiation field?

No.

Once something removes energy form the rear, there is no more energy to
excite and further elements. You can't excite additional reflectors
because there is no energy there to excite them, and so they become
useless hunks of metal without much current.

Why are there no designs with just one director, and multiple
reflectors?

Because it doesn't do anything when you put an element in an area where
there is no field to excite it.

Why does the shorter element apparently affect the field
more than the longer elements?

They don't. They just happen to be where energy has been concentrated,
and as long as they are being excited they can help shape the pattern.

73 Tom