Henri Wilson replied to Leonard Kellogg:

well please spell it out in a way that we can all understand..

I thought I had. Re-read the longish paragraph above and
see if it makes sense. If it does, then try to explain to
yourself why it must be that way.

You state, "The more rapidly the light bunches, the shorter
the unification distance."

I would like that to be true but you don't state why it
should happen.

Yes. Your response is more to the point than you imagine.

Unfortunately, I don't know how to explain why it should
happen. It is only a minor aspect of a much greater whole,
and you need to comprehend the whole in order to be able
to see the parts. Try to make the most of what little I
and others can provide. George especially has given you
far more than I can, but you need to make use of it. Even
Androcles has given you useful knowledge, if only you will
put it to use.

You told George that the way the light curves of variable
stars are measured over a number of cycles and then averaged
together 'sounds pretty suspect'.

I replied:

It is an elementary school level problem.

It is like measuring your height once an hour during the
day for a week, then averaging the measurements together.
You measure your height immediately after arising, again
an hour later, and so on. After a week you sum all the
measurements made just after arising and divide the result
by seven, then you sum all the measurements made an hour
after arising and divide the result by seven, and so on.
When you graph the results you have a chart showing how
your height changes during the day.

The averaging process you say 'sounds pretty suspect' is
used every day in millions of businesses around the world.
It is even simpler and more basic than the fundamental
principles of algebra. Almost any sixth-grade student
could demonstrate it for you.

That's nothing at all like 'epoch matching'.

The epoch matching is integral to the process whether you
are graphing your height or the luminosity of a star. It
does depend on judgement but it is so intuitive that it
seems very strange that anyone would object to it.

This doesn't prove anything one way or another, but many
years ago I converted a computer program from Apple II
format to DOS at the request of the American Association
of Variable Star Observers. Its purpose was to assist
astronomers in epoch matching. It was a very simple
program and merely allowed one to do on a computer what
could be done by plotting observations on a sheet of
tracing paper and moving it side-to-side.

This is the problem. Accorbing to the BaTh, it appears that
the unification distance of light from short period binaries
is a lot less than that from long period ones. This may not
even be true but if it is, I want a physical explanation...
can you provide one?

Yes. George Dishman told you yesterday that he knows why
there is a connection between the period and the unification
distance. I know, too. He declined to say what that
connection is. I am going to decline, as well. However, I
gave you a clue on 18 February, which I repeated 20 March,
and will repeat again now:

The things which are closest at hand can sometimes be the
most difficult to see.

I gave you that clue specifically to help you discover the
connection between orbital period and unification distance.
Or more precisely, the connection between bunching rate
and unification distance.

Well, we know bunching rate is dependent on orbit speed

Be more precise. Exactly what is it dependent on?

What does the bunching rate depend on when the light is
emitted by a police LIDAR or RADAR speed measurement device
and reflected back to the detector by a moving vehicle?

What does the bunching rate depend on if the source is a
powerful lamp being swung around at high speed on the end
of a cord, by an astronaut in a spacesuit, light-years
away from us and the nearest star?

What does the bunching rate depend on if the source is a
distant searchlight out in space, aimed at us, bouncing
back and forth toward and away from us on a spring?

but the only assumption I would make about unification rate
at this stage is that it should be solely a property of the
space through which the light is traveling.

Although that assumption seems unassailable on its face,
it would be best not to make it. There are other
possibilities. You need to be aware of the range of
possibilities in order to see the whole picture.

It is hard to see how your claim can be correct because
during the process of unification, fast photons have to
slow down ...in which case bunching also slows.... just
as it would if you started with that situation.

This is another observation which is more to the point than
you are aware. It can help lead to the answer.

Still, there might be a more subtle connection...I hope
there is.

Be careful what you wish for.

The connection is actually quite obvious once you see it.
That will only come about when you comprehend the whole
picture of what you are trying to do and what you are in
fact doing.

Leonard