Why does the acquired immune system discriminate self from nonself
using a nonself representation?

One of the problems addressed by the acquired immune system is
interesting nonself from everything else (novelty detection) (assuming
the classification decision occurs within a hyperspace of whatever
attributes are involved in receptor
structure/binding/specificity/whatever). This simplification can be
further reduced to the modelling of a probability density function for
antigens of interest (potentially harmful) and everything else. Simply
put B lymphocyte cells and T lymphocyte cells can be considered
detectors in the interesting-nonself (pathogen) hyperspace.

My question is why model the discrimination problem in the complement
(nonself) space? Rephrased: what are the advantages of using a nonself
representation for detectors (closeness in specificity) over a
self-based representation (distance in specificity)?

I assume that the model of self used to prepare things like T
lymphocyte cells in the thymus and B-cells during clonal selection is
a pretty good approximation of what the detectors will encounter of
self in their lifetime. Thus, the model of self is useful, and this
implies that the decision boundaries for what is self and nonself are
somewhat known. Further, I assume the size of the self hyperspace is
smaller than that of potentially harmful pathogens.

I have to assume that the reason has to do with biochemical properties
such as it is efficient to combine detection and response
(touch-detect-bind-proliferate?) I am clearly no biologist and the
little ?knowledge? I have of the immune system is clearly a dangerous
thing ? though given all my dangerous assumptions and reductions, I
believe my question is relatively straightforward, yet the books on
immunology do not seem to have a straightforward answer theoretical or
otherwise.

First, receptor structure is defined by what amounts to a random
selection of genetic components, with a very large number of possible
combinations.   During lymphcyte maturation (ignoring auto-immune
disease), self-reactive lymphocytes are selectively deleted.  That is,
during that process, any lymphocyte that finds a ligand for its
receptor dies.  That leaves only lymphocytes that have not found
matching ligands.  These are the ones that form the basis for an
immune response if, after maturation, the DO find a ligand.  The
receptor structures are random - there is no model of non-self
involved.  Many will never find a ligand at all, and there is no
guarantee that there will be a lymphocyte with a receptor that will
bind an epitope on any given foreign protein.  The receptor diversity
possible, coupled with the wonderful antigen-presentation systems in
cells make for a wonderfully sensitive and responsive system.  This is
not without its downside, as the generation of antibody diversity is I
think the only normal cellular process where double-strand DNA breaks
are made.  This is an inherently risky process, and when it goes
wrong, leukaemia can be the result.  The pros and cons have been
weighed in the evolutionary balance, and what has resulted is a
marvel.

Well - that was fun to write, but I'm not sure if I addressed your question.

Thank you for your question.  
 
However, I believe that to answer it well, your question will require
more time and effort than the average amount of time and effort
associated with this price. Here is a link to guidelines about pricing
your question, in the pricing guide:
https://answers.google.com/answers/pricing.html

Thanks for the advice, I have since bumped the price/cost up.