  We consider the non-supersymmetric "magic" theories based on the split
quaternion and the split complex division algebras. We show that these theories
arise as "Ehlers" $SL(2,\mathbb{R})$ and $SL(3,\mathbb{R})$ truncations of the
maximal supergravity theory, exploiting techniques related to very-extended
Kac-Moody algebras. We also generalise the procedure to other
$SL(n,\mathbb{R})$ truncations, resulting in additional classes of
non-supersymmetric theories, as well as to truncations of non-maximal theories.
Finally, we discuss duality orbits of extremal black-hole solutions in some of
these non-supersymmetric theories.
