[R-sig-ME] [R] understanding I() in lmer formula

[Don Cohen]

Ben Bolker writes:
 ...
 > term), but so far my guesses haven't panned out.  This is the
 > reason we keep asking for a **reproducible** example; if I could
 > run this example myself I could almost certainly figure out what's
 > going on, but remote debugging is really hard.

If it were easy to produce a minimal example I'd have done it to
begin with.  I was hoping to get some useful information with less
work than that.  And it seems I've succeeded.
 ...
 > problem, it can be worked around by defining a new variable rather
 > than constructing it on the fly (this is what I suggested in my
 > previous error).
I understood that, but editing the already parsed formula seems 
a much better work around for now. 

 > > What all this is supposed to mean is another topic I'd also like
 > > to discuss.

Admittedly this is a different topic, but it is at least related:
Can someone tell me (or tell me where to find) what || means as opposed
to | ?  I've seen the "answer" in the paper on "Fitting Linear 
Mixed-Effects Models using lme4" (I notice Benjamin Bolker is one of
the authors - I must have finally found the right place to ask!) that
says || is uncorrelated random slope and intercept and | is correlated,
but so far that doesn't make any sense to me.
Where is this correlation in the model?  Is it something to be estimated
or something given or something else?  Is it part of what is to be
minimized in fitting the model?  In fact, it would help me a lot to know
exactly what IS being minimized.  The paper above probably does answer
this question, but I seem not to have the background required to 
understand it, and it's not yet clear where to get that background.
Last time I tried reading it I gave up around eqn 16.  I thought I was 
understanding significant parts, but there were by that time enough
questions to make it impractical to try to continue.
I tried to construct some simple examples and found that | seemed to be
doing what I expected (or at least close), whereas I have no idea how
to account for the results I got from ||.

 > OK, I've been able to reproduce this (code below), will dig in and let
 > you know what I find.

Thank you.  
If I've found a bug then I'm glad to have been of at least some use.