In all branches of theoretical physics a key part
of any good prediction is a careful assessment of the theoretical
error which the prediction carries. Such an assessment is a
precondition for any detailed quantitative comparison with
experiment. As is clear from numerous examples throughout physics,
this assessment of error usually is reliably determined based on an
understanding of the small quantities which control the corrections
to the approximations used when making predictions. Perhaps the
most famous example of such a small quantity might be the
fine-structure constant, , which quantifies the
corrections to electromagnetic predictions of elementary particle
properties or atomic energy levels.