  This paper forms part of a wider campaign: to deny pointillisme. That is the
doctrine that a physical theory's fundamental quantities are defined at points
of space or of spacetime, and represent intrinsic properties of such points or
point-sized objects located there; so that properties of spatial or
spatiotemporal regions and their material contents are determined by the
point-by-point facts.
  More specifically, this paper argues against pointillisme about the structure
of space and-or spacetime itself, especially a paper by Bricker (1993). A
companion paper argues against pointillisme in mechanics, especially about
velocity; it focusses on Tooley, Robinson and Lewis.
  To avoid technicalities, I conduct the argument almost entirely in the
context of ``Newtonian'' ideas about space and time. But both the debate and my
arguments carry over to relativistic, and even quantum, physics.
