  We consider the polarization of unstable type IIB D0-branes in the presence
of a background five-form field strength. This phenomenon is studied from the
point of view of the leading terms in the non-abelian Born Infeld action of the
unstable D0-branes. The equations have SO(4) invariant solutions describing a
non-commutative 3-sphere, which becomes a classical 3-sphere in the large N
limit. We discuss the interpretation of these solutions as spherical D3-branes.
The tachyon plays a tantalizingly geometrical role in relating the fuzzy S^3
geometry to that of a fuzzy S^4.
