Spacetime supposedly started as a singularity at the initial big bang. Most models of the universe also attribute to it an infinite radius at present. To look back to the cosmological origin means looking outward through boundless space at an entity which was once pointlike but now seems to span the sky boundlessly. Is infinite spacetime of a reciprocal duality to that infinitesimal? Could have extensive spacetime unfolded from a unique value in a preexisting 4-space? Might spacetime evolve from three spacelike and one timelike particles?