Abstract: The climate for nuclear arms reductions has changed positively in recent years with the statements of the "Gang of Four" (Kissinger, Schultz, Perry and Nunn) that there is a credible path to zero, the ratification of the NEW START Treaty, the successful review conference for the Non-Proliferation Treaty, and the resubmission for ratification of the CTBT. Jay Davis, who served as an UNSCOM inspector in Iraq after the first Gulf War and as the head of all US inspection processes as first Director of the Defense Threat Reduction Agency, recently lead an APS/POPA study on the technology needs for future arms control treaties. However, in addition to technology, many other issues matter as the number of nuclear weapons is decreased. Among these are changes to theories of deterrence and the nuclear umbrella over non-nuclear states, the lesser granularity of military platforms that support the weapons, increased credibility of missile defensive systems, and the coupling of conventional and nuclear weapons, among others. Davis will walk the audience through a progressive set of weapons reductions that illustrate these points. Comparison to either Zeno's Paradox or Dante's Circles is discouraged. The talk does however end with an interesting technical proposal for evaluation.