  The famous singlet correlations of a composite quantum system consisting of
two spatially separated components exhibit notable features of two kinds. The
first kind consists of striking certainty relations: perfect correlation and
perfect anti-correlation in certain settings. The second kind consists of a
number of symmetries, in particular, invariance under rotation, as well as
invariance under exchange of components, parity, or chirality. In this note, I
investigate the class of correlation functions that can be generated by
classical composite physical systems when we restrict attention to systems
which reproduce the certainty relations exactly, and for which the rotational
invariance of the correlation function is the manifestation of rotational
invariance of the underlying classical physics. I call such correlation
functions classical EPR-B correlations. It turns out that the other three
(binary) symmetries can then be obtained "for free": they are exhibited by the
correlation function, and can be imposed on the underlying physics by adding an
underlying randomisation level. We end up with a simple probabilistic
description of all possible classical EPR-B correlations in terms of a
"spinning coloured disk" model, and a research programme: describe these
functions in a concise analytic way. We survey open problems, and we show that
the widespread idea that "quantum correlations are more extreme than classical
physics allows" is at best highly inaccurate, through giving a concrete example
of a classical correlation which satisfies all the symmetries and all the
certainty relations and which exceeds the quantum correlations over a whole
range of settings
