  Using elementary equalities between various cables of the unknot and the Hopf
link, we prove the Wheels and Wheeling conjectures of [Bar-Natan, Garoufalidis,
Rozansky and Thurston, arXiv:q-alg/9703025] and [Deligne, letter to Bar-Natan,
January 1996, http://www.ma.huji.ac.il/~drorbn/Deligne/], which give,
respectively, the exact Kontsevich integral of the unknot and a map
intertwining two natural products on a space of diagrams. It turns out that the
Wheeling map is given by the Kontsevich integral of a cut Hopf link (a bead on
a wire), and its intertwining property is analogous to the computation of 1+1=2
on an abacus. The Wheels conjecture is proved from the fact that the k-fold
connected cover of the unknot is the unknot for all k. Along the way, we find a
formula for the invariant of the general (k,l) cable of a knot. Our results can
also be interpreted as a new proof of the multiplicativity of the
Duflo-Kirillov map S(g)-->U(g) for metrized Lie (super-)algebras g.
