  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 concept
of velocity in classical mechanics; especially against proposals by Tooley,
Robinson and Lewis. A companion paper argues against pointillisme about
(chrono)-geometry, as proposed by Bricker.
  To avoid technicalities, I conduct the argument almost entirely in the
context of ``Newtonian'' ideas about space and time, and the classical
mechanics of point-particles, i.e. extensionless particles moving in a void.
But both the debate and my arguments carry over to relativistic physics.
