Throughout the Cenozoic the Earth experienced global cooling that led to the appearance of continental glaciers in high northern latitudes around 3 Ma ago. At approximately the same time, cold surface waters first appeared in regions that today have intense oceanic upwelling: the eastern equatorial Pacific and the coastal zones of southwestern Africa and California. There was furthermore a significant change in the Earth's response to Milankovich forcing: obliquity signals became large, but those associated with precession and eccentricity remained the same. The latter change in the Earth's response can be explained by hypothesizing that the global cooling during the Cenozoic affected the thermal structure of the ocean; it caused a gradual shoaling of the thermocline. Around 3 Ma the thermocline was sufficiently shallow for the winds to bring cold water from below the thermocline to the surface in certain upwelling regions. This brought into play feedbacks involving ocean-atmosphere interactions of the type associated with El Ni¿o and also mechanisms by which high-latitude surface conditions can influence the depth of the tropical thermocline. Those feedbacks and mechanisms can account for the amplification of the Earth's response to periodic variations in obliquity (at a period of 41K) without altering the response to Milankovich forcing at periods of 100,000 and 23,000 years. This hypothesis is testable. If correct, then in the tropics and subtropics the response to obliquity variations is in phase with, and corresponds to, El Ni¿o conditions when tilt is large and La Ni¿a conditions when tilt is small.