The Pillar of Speed is a Pillar made available by having the Arcana of Agility starting technology (by researching in Era I with ELCP). The Pillar of Speed decreases the Movement Cost of tiles in an area around it; the intensity and area of the effect are based on the pillar's Arcana level. Paved Roads, however, are not affected by the Pillar of Speed, and will remain at whatever their Movement Cost is, which can lead to the strange situation of paved roads costing more Movement to traverse than the terrain around them if a Pillar of Speed with an Arcana level of 2 or higher has been placed near a road and Endless Mechanisms has not yet been researched.
Note: In ELCP Pillar of Speed only lasts 2 turns but cost got reduced by 70%, because in most situations a short duration cheaper speed boost is preferable.
Upon obtaining the Cold Engineering technology by completing Chapter 5, Part 1 of the Ardent Mages faction quest, the Pillar of Influence will decrease Movement Cost on tiles within its range by an additional 50% during winter, but will not decrease movement speed by more than 75%, thus making this effect largely pointless after the first Arcana level.
The Dust magic around this pillar grants passing Mages an extra fleetness of foot, reducing movement costs.